is it possible for a 19 year old to rent an apartment by herself?

Absolutely! In fact, once you turn 18 you can get an apartment legally, because you are legally old enough to enter into a binding contract. Also, fair housing prohibits a landlord from discriminating against you because of your age. (Once you are legally able to enter into a binding contract.)

Keep in mind that as a first time renter, you may have to pay a much higher deposit or get a co-signed/guarantor.

Depending on where you try to rent and/or from whom, there are several things they could look at to make a decision.

1. Credit

2. Income - usually need to make 2.5 - 3.5 times the monthly rent

3. Previous rental history

4. Employment stability

I can tell you with the company I work for, we have rented to many first time renters. Please do yourself a favor, and stay responsible. Don't use your own place as the time to break all the rules. It will come back to bite you.

I think it's great that you are already planning for your future. I wish you the best of luck!