Whether you will need an appointment to get passports at the post office varies by post office. (And remember, not every post office does it at all.)
Near us, there was one that required appointments at all times, one that never did, and one that didn't if it was a weekday, but did need an appointment if you wanted it to be on a Saturday.
Also, you don't mention a father of your daughter. Most of the time, they either want both parents to attend or for the second one to fill out notarized paperwork in advance. If he is completely out of the picture, you may want to call them ahead of time to make sure you have the proper documentation. My apologies for telling you this if you already know it, but I just didn't want you to be surprised when you got there.