K.,
You can. However, there are rules.
1. If your husband, father of the child, will not be with you when you go to 676 19th Street NW, Washington, DC - You MUST have a signed form from your husband, and you MUST have his drivers license copy - the document that was used to notarize the Form DS-3053.
2. You MUST have your child with you.
3. You MUST have proof of travel. And it MUST be within 48 hours or the guards will turn you away.
You must have ALL paperwork with you.
Marriage License
Birth certificate
DS 3053 - http://www.state.gov/documents/organization/212243.pdf
Application - http://www.state.gov/documents/organization/212239.pdf
TWO passport pictures
Park in the George Washington Campus garage on 21st street & H - it's $22 for the day - and you will NEED IT. DO NOT PARK ON THE STREET!! There is NO street parking before 9:30. And even then it's 2 hour parking. If you "need" same day service - plan on being there at LEAST 8 hours.
We had a mistake on our form - this is why I know about this personally. The notary who "notarized" my husband's signature used the date "2014" instead of "2015" - so we had to get it fixed and the appointment time for the post office was going to be AFTER our travel...
If you are NOT traveling to Europe or The Middle East? You can get a passport card - which is good for Mexico and Canada. However...if your travel is eminent? they are NOT processed in DC - they are processed in Arizona...and you won't get it for 2 weeks.
You will be charged a $100 EXPEDITE FEE for this - they accept Visa, Mastercard, AMEX, cash and check. The cost of the passport $85. It will be $185 for your child's passport.
before you do this - find out the rules on where you are traveling to. They will ask you there as well. And if you aren't prepared? They WILL make you start all over again...
The passport office in DC is next to a book store, so you don't have to wait IN the office. However, no food or drinks are allowed in the passport office. They will allow bottle for children. There are TVs, however, they are stuck on CNN or news. So bring something for your child to do.
My son and I took a cab to the Jefferson Memorial and had lunch there. It was a long day. So glad we parked in GWU and was able to walk everywhere.