Baby Florence Rose Endellion appeared unfazed by the bank of photographers and camera crews as she was cradled by the Prime Minister and his wife on the steps of No 10.
Florence was wearing the shawl made by Jane Fraser-Cross, from Sutton Coldfield, Birmingham, a fundraiser and grandmother of 10, who likes to be known as "Granny Jane".
Mrs Cameron, who was wearing an orange dress, smiled when asked if they were being kept awake and said: "Yes."
Florence opened her eyes briefly when Mr Cameron bent to kiss her on the head.
She was born at the Royal Cornwall Hospital in Truro last Tuesday, weighing 6lb 1oz.
She was not expected until this month, but caught the family by surprise while they were on holiday. Her middle name, Endellion, refers to the village of St Endellion on the north Cornish coast, near where the Camerons were staying.
The Camerons are also parents to Nancy, six, and Arthur Elwen, four.
The couple lost their other son, Ivan, who suffered from cerebral palsy and severe epilepsy, when he died aged six last year.
Mrs Fraser-Cross said she was "absolutely thrilled" the family liked her gift.
She said: "I'm so elated. I'm absolutely thrilled because I admire David Cameron and after all the sadness they went through a few months ago. I feel honoured."