They each shot six-under-par 66 in perfect conditions on the Majlis Course to end the day one stroke ahead of the defending champion Shanshan Feng from China.
Dame Laura Davies and Elisa Serramia of Spain carded rounds of four-under-par 68 to lie a stroke further behind.
Doncaster's Rebecca Hudson birdied two of the last four holes on the inward nine for a one-over-par 73.
After retrieving a dropped shot at the second immediately with a birdie at the third she bogeyed holes five, 10 and 12 before finishing strongly.
Young, who finished fifth in the event 12 months ago, is bidding for her first professional title after a string of top-10 finishes including another fifth place recently in India.
The 33-year-old from Hampshire, who plays out of Brokenhurst Manor Golf Club in the New Forest, opened with four straight birdies from the 10th and added another at the 18th. The long hitter had three more birdies and two bogeys on the front nine.
The €500,000 Omega Dubai Ladies Masters is the finale to the Ladies European Tour season. Co-leader Alonso is yet to make a cut from five tournaments played in 2015, but a strong finish would be the perfect end to a difficult year.
World No 6 Feng carded five birdies in her bid to win the title for the third time, having triumphed in 2012 and 2014.
Davies had 27 putts in her 68 and was happy to be in contention for her 80th official tour title.
She said: “I feel like it's a course I should do well on. The first few years, I think I finished second, third and fourth. Since then I've had some missed cuts and average finishes. It's a course I would like to think I could do well on. This is a good start but that's all it is - a good start.”