In her traditional message to the nation, the Queen also made an observation about the future for new parents - "life will never be quite the same again".
Delivering her message the Queen said: "Here at home my own family is a little larger this Christmas. As so many of you will know, the arrival of a baby gives everyone the chance to contemplate the future with renewed happiness and hope.
"For the new parents, life will never be quite the same again."
These words were accompanied by footage of William bouncing George up and down in his arms, with Kate by his side, outside the Chapel Royal, St James's Palace, ahead of their son's christening.
The main theme of the Queen's seasonal message was reflection and she looked back over the past 12 months to the 60th anniversary of her coronation.
Those not with their families this Christmas were in the Queen's thoughts, from servicemen and women abroad to emergency service workers.
Speaking about members of the armed forces serving overseas, the Queen said: "We are forever grateful to all those who put themselves at risk to keep us safe."
Looking forward to the 2014 Commonwealth Games in Glasgow, the Queen said: "The baton relay left London in October and is now the other side of the world, on its way across 70 nations and territories before arriving in Scotland next summer."
Images were shown of Olympic gold medallist Sir Chris Hoy holding the baton, then footage of it making its way around the globe.
The Queen said: "Its journey is a reminder that the Commonwealth can offer us a fresh view of life. My son Charles summed this up at the recent meeting in Sri Lanka. He spoke of the Commonwealth's 'family ties' that are a source of encouragement to many.
"Like any family, there can be differences of opinion. But however strongly they're expressed, they are held within the common bond of friendship and shared experiences."
Meanwhile Prince George had a "lovely" first Christmas but stayed in the warm as the Royal Family attended their traditional Christmas Day service. The Duke and Duchess of Cambridge made the journey to St Mary Magdalene Church on foot holding hands.