My daughters both learned on Honda CRF/XR50 & 70's, then moved up to an XR/CRF 80's & 100. Now on a Yamaha TTR 125LE and a CRF150F, with a few rides on a YZ 85.
Mine are 15 & 17 now, and started younger than your daughter. At 11, she could ride an XR/CRF 80. The Honda kids bikes are as reliable as a rock, and pretty light, too. Air filter, oil, chains & tires will be all you'll tend to before she outgrows one.
I have taught dozens of kids to ride. It's tough to beat the Honda XR/CRF series, for growing riders, even though I have a fleet of Yamahas. I think each bike I've sold only cost me a couple of hundred $$, net, to own & ride. Still have the 70 & 80, just for teaching other kids on.
Good luck & have fun! :cool: :ride: