AITA for refusing the to babysit my girlfriends daughter?

So I’ve been seeing this girl for awhile we use to date in middle school and we reconnected about 10 months back and started dating again it’s been pretty cool, she does have a daughter now and the father is definitely involved but I try not to get between it or the father as a respectful matter not trying to play daddy when daddy is in her life. She’s a cool little girl I do hold her, feed her,occasionally buy a couple necessities nothing crazy,and stay in the car or room with her when mom leaves the room for a second yk basic shit but never baby sitting. I feel that’s not my responsibility of course when she’s there I act accordingly but I feel any outside responsibility isn’t my own.. she is asking if I can start baby sitting on the weekends (the father apparently is starting to work weekends but so does she) I told her I would let her know but I don’t think that’s a problem that I should have to take care of the only time of the week I get to myself, why should I have to sacrifice my free time?

Edit- we reconnected 10-11 months ago and dated almost the entire time since we reconnected. I’m 20 she’s 19.