OK. IMO, 11 isn't too late. I've seen kids catch up remarkably quickly and do very well, even starting older. The problem is most clubs are oversubscribed and don't have the room for older inexperienced gymnasts. It's a matter of finding someone to give your DD a chance..
Competition wise there are three routes she can follow;
Floor and vault. Advantages are lower hours (usually 4-6 a week), she will progress faster as she's focussing on only two apparatus. Probably the best idea if she's going into secondary school too..
Artistic. Floor, bars, beam and vault. This is regional competition generally, against other clubs. Hours are likely to be a lot higher- if you're in a competitive region could be around 20 hours a week. Some clubs do well on 9-12 though.
Elite. No chance really. The kids here are picked at 6 or 7 and train 18-20 hours a week from then. By 11 they are looking at international competition and 30 odd hours a week. You'd have to be some sort of freak to catch up…
First step is to speak to the coach at your club and see what they offer. If they can't help, ring around a few other clubs and see if they'd be willing for your DD to try out for a competition squad. The best plan is sometimes to look for the smaller clubs that focus on general (F+V) as the big clubs are very selective.
She could also look at sports acro, tumbling, trampolining, diving, or even rhythmic gymnastics clubs. Some have a higher tolerance for age if she shows potential.