Have you considered (both going from and back to Heathrow) taking the train itself? You may not only have more luck, but if this is your first trip to London, the tube can get EXTREMELY packed, and you may find yourself with luggage and infant being squeezed into a situation where you have no breathing room, and you can pre-purchase, I believe, tickets for the train, and if it does not stop close to where you're staying, it will surely stop somewhere closer to your hotel and shorten the trip on the tube. But if that is not available, I would definitely choose a taxi over the tube with your particulars. I always take the train from the airport and back, and always hate taking the tube anywhere, but in your case, with the immense numbers of people who seem to always be on the tube, it would be horrible if you had your luggage taken or your child injured. Good luck to you, and enjoy England, it's so beautiful at Christmas.
