I just had a baby a week ago. Do you think I could ask for a letter for her?
First off, congrats on the new baby! : )
And to answer your question: of course! Send the baby's name, address, and birthdate to:
The White House
Attn: Greetings Office
Washington, D.C. 20502-0039
See http://www.whitehouse.gov/greeting/ for more details.