How long does your baby nap for?

Amy
My baby is 2 and a 1/2 months old. I've been timing her naps and keeping track of the time she's awake just to get her on a schedule with having her take 2 hour naps max. 
I've noticed her trying to fall back asleep whenever I wake her up from the two hour naps so I've been letting her nap up to 3 hours. Do you think that's fine?
Everything online says wake her up after 2 hours or so, plus I don't want to mess with her nighttime sleep because she's been doing so great at sleeping through the night ! 
How long do you have your babies nap for?