Thank you notes are a lost art. First, just remember that ANY note you write will be appreciated.
If you don't know what to say, choose a card that has a pre-printed sentiment. Simple thank you cards can be found on most card racks. It just takes a little looking. Then, sign it with something like: "You have helped bring so much joy into our lives."
If you want to hand-write the entire note, the following formula is often suggested for thank you notes:
1. Mention the gift and occasion. (in this case, the gift is your baby, or the gift of the doctor's time)
2. Name a specific, positive detail about it. (this might be the doctor's attitude, or the joy that having a bay brings)
3. Praise the giver in some way
4. State how the gift will be appreciated in the future.
If you write one sentence for each of these four items, you will have a nice little note. Use a smaller card if you are afraid your note won't be long enough.
No matter what you write, I guarantee you that the doctor will be very glad to receive it.