I started level 4 at 11 and know girls who did it even later and competed level 10 and NCAA. Gymnastics classes will also be a good base if you choose to pursue tramp and tumbling, acro, cheerleading, or any other sport as a teenager. Go for it. If you're in the US, you can use this link: Begin Here. Go Anywhere. and click on "Begin Here" at the top to enter your zip code and find a gymnastics club in your area.
Oh definitely it's fine. Older gymnasts sometimes succeed faster because they can pay attention for longer periods of time, have more drive, and understand more. One former elite, Krista Jasper maybe, progressed level 4 to elite in four years! Anything can happen.
It's never too late. Also, when you start a bit older your body hasn't been worked as hard at such young ages which may be a plus. Eleven years old is definitely not to old to start. Go for it!!!!!!!! Plus if she is flexible--she has a head start on a lot of skills.
I started at 13, with a lot of flexibility and a bit of strength. I was stubborn and wanted to be good, so I got pretty far ... I say go for it, as long as you desire something you can ALWAYS try and go as far as you're willing to work!