I would go for the adult version of the bike you would buy for her if you were buying a new kids bike.
There is a whole range of bicycles for small adults which are basically not that different from kid bikes, just bigger.
If your bike shop does not have something you find fitting (for a girl her age) search on.
I live in the Netherlands where a lot of children are tall but we still have smaller adults who are in the same size range. Bikes fitting adults also fit children who are the same size.
It may well be that in a few years you will buy her a new bike again, fitting her adult size. So consider her 'new bike' as a further kids bike which happens to be an adult size frame.
If in your area gears are needed, get a bike with enough gears for her, at 11 she is old enough for two sets of gears, but do teach her how to use them.
In the Netherlands most kids get new bikes before going to secondary school, that is around 11 or 12 years old, and most of those bikes are very sturdy, as school bike sheds are hard on bikes.
Most of those bikes are adult frames in the smaller ends of the range (although some of those kids are already as tall as the average adult.)
If your child will not cycle to school, only for fun or only with you, you can select the bike based on that, and keep an eye on it as well.
An other thing the average teen in the Netherlands has to face is lessons in bike repair and maintenance. I have been patching my own tubes (and replaced the tyres) since I was not yet 12 and I was certainly not the only one in school who did.