My sister's no liar, but when she warned me that Australia might be cold and rainy, I really didn't believe her, even though she's lived there for the last three years.

We were travelling in November – Aussie springtime – so surely her idea of bad weather was like a warm shower compared to wet and windswept Yorkshire? She spoke the truth and I still have the woolly jumper, bobble hat and brolly I bought in Sydney, and they are a reminder that there are many misconceptions about the land down under. One is that it is always hot and sunny. It isn't. Another is that you can't move for kangaroos. The only Skippy we saw was in Sydney zoo, and yet another is that all Aussies are laid back and friendly. They're not always. Sydney airport was a good example of the latter. Unfriendly and intimidating staff barked orders and interrogated us.

The Sydney welcome was a culture shock because we'd flown with Singapore Airlines from Manchester and although I hate flying it was the best long-haul flight I've ever experienced. The staff anticipate your every need, are equipped with permanent smiles and there's 24-hour entertainment and a seemingly constant supply of meals, drinks and snacks. Our two 10-year-olds would have stayed on board for a fortnight if we'd let them. We'd also had a two-day stopover in Singapore where the people are equally smiley, friendly and helpful.

It's a great place to break a long plane journey (stopovers are usually free) especially with children because it is so clean and virtually crime free. That's thanks to an authoritarian government that has transformed this tiny island from shanty towns to skyscrapers and a world renowned financial centre.

Freedom is the price the natives pay and there are rules for everything, like no spitting, no chewing gum. "But we have good homes and jobs," one Singaporian told me, adding that those who can't live by the rules tend to leave. Good hotels are inexpensive. Again on my sister's recommendation, we stayed in Swissotels at Clarke Quay, which has splendid pools and is very child-friendly. The quay at night is like fairyland and teeming with interesting bars, including one hospital-themed venue with wheelchairs for seating. On the way back we stayed at the Stamford, another Swissotel close to the famous Raffles hotel and linked to a huge mall.

Shopping is a national pastime and the air-conditioned malls are great, though we preferred the chaotic markets in China town. Another pastime there is eating out and the food is excellent and inexpensive.

In fact, food was a highlight of the whole holiday.

The food in Australia is also fabulous and fresh and the best we ate was at Palm Cove, a village that is now devoted to holidaymakers.

It's where, after an internal flight from Sydney to Cairns, we started our travels in Australia. Like almost everyone else, we were there to see the Great Barrier Reef and the rainforest – and they really are a must.

We'd found Palm Cove on the internet, where it was sold as an idyllic location for honeymoons and holidays, and it truly is. The beaches there are beautiful and the restaurants are beachside. In the evening, with the sun setting on the surf, it is paradise. While paradise usually costs a fortune, we managed to find a budget priced Novotel there, which was great value with access to an Olympic-sized pool five minutes' walk away.

Be warned that walking, even for the super fit, isn't easy in the daytime. It's scorching hot and humid in Queensland.

We took the easy way out and booked organised tours to the Barrier Reef – rightly one of the seven natural wonders of the world and absolutely amazing.

We also did a tour taking in Hartley's crocodile farm and Kuranda, a very touristy rainforest village. The village was reached by an old-fashioned steam train through the rainforest and our descent was via a cable car that offered spectacular views. Kuranda is one of the few places we saw indigenous Australians.

The other was at the main ferry terminal in Sydney, where they were covered in body paint and played their didgeridoos under the watchful eye of minders collecting Aussie dollars.

Most aboriginal people seem to be ghettoised away from the tourist trails. They, and their social problems, are a depressing reminder of a great injustice, but at least new PM Kevin Rudd has finally apologised for the horrors.

One of Rudd's most fervent supporters was Russell Crowe and thanks to having my sister as a tour guide, we saw his penthouse in Woolloomooloo, a posh suburb of Sydney and ate at Harry's Café de Wheels – a famous pie van selling pie and peas. If you go there after dark you can eat your pie by the waterside and watch the flying foxes – fruit bats – that have colonised the nearby Botanic Gardens. We spent almost two weeks in Sydney, based mainly at the Novotel Darling Harbour. Sydney hotels are expensive and this offered good value and a central location. There's an incredible amount to see and do. We went back to the Botanic Gardens in the day to see the bats hanging from the trees and walked to Mrs McQuarie's point, which gives one of the best views of the harbour. The path at the edge of the gardens takes you to the Opera House – an architectural highlight.

Other high points included the posh suburb of Paddington, where there are some great independent shops and quaint Victorian houses, and the numerous ferry trips you can take from Circular Quay. The ferry to Watson's bay offered a great walk around the cliffs, where you can sometimes see whales, and ended at the excellent fish and chip shop. The children loved Luna Park, a small 1950s style theme park and we all enjoyed Sydney zoo. The ferry to Manley gave us the best pictures of the Opera House and the bridge and allowed us to see champion surfers in action.

It's there we were swept off our feet by the incredibly powerful waves. Naturally we stayed between the flags watched over by lifeguards, though most Aussies seem to ignore them along with the dangers of riptides, sharks and box jellyfish. If you're based in Sydney, it's just a couple of hours' drive or train ride to the spectacular Blue Mountains. They are a must-see. It's there we saw our one and only spider, a huge, hairy Huntsman. It was non-poisonous, but there are plenty of arachnids that are and we were fastidious about checking our beds and shaking out our shoes.

Australia is a dangerous place, but it's also beautiful, magical and totally fascinating and we desperately want to go back and see some more, a hankering I never expected.

It's a trip I had many reservations about, not least because it cost the earth, in every sense. Our carbon footprint last year was enormous and our savings completely blown on three weeks that cost well over £6,000 for the four of us. But it was worth every penny.

Getting there:
We flew with Singapore Airlines from Manchester and booked as soon as the flights were released for the best deal.
They cost about £700 each including stopovers in Singapore. The service is superb. Singapore Airlines, www.singaporeair.com
In Singapore, we stayed at Swissotel, Merchant Court, Clarke Quay and The Stamford, www.swissotel.com
In Palm Cove, we found the Novotel was good value, www.novotel-pcr.com.au and we also used Novotel in Darling Harbour, Sydney, www.novoteldarlingharbour.com.au