Is my mum right or is she just being selfish?

The short story is I've got an 8 year old kid (yes I'm 22 you do the maths) and my parents have raised her since she was born. But we always agreed I'd have her back when I could. Well now I have a good job and a lot of savings and a two bedroom flat not far from my parents house but my mum doesn't want me to take her. She puts off the conversation and constantly says "you can have her when she turns 13". She thinks she's funny but seriously I just want her back now. She's my kid and I've worked hard to get to this point just so I can have her and be her mum but my mum won't even let me tell her I'm her real mum. I don't want to wait until she's older and I think it'd be easier for her to adjust now but my mum disagrees and now I don't know what I should do >_<