well you know, 11hrs overnight is actually fine - many babies never sleep 12 hours overnight and 11-11.5hrs is a full night for them.
You could try wake to sleep but to be honest if she is asleep at 6.30, then 5.30 would be a reasonable wake up time. The other thing you could try is giving her a 'dream feed' bottle at some point during the night, and see if she will then sleep through the 12 hours. Many babies are still having one night feed at this point, it's perfectly possible she may just be waking because she's hungry.
I know that over tiredness is a worry, but be wary of under tiredness too. Yes you can reinforce early wakings by putting down for a nap too early. She probably needs at least 3hrs of A time - maybe 3hrs 15 or even 3hrs 30 - and under tiredness can be cause of early waking, too.