I think that the number of hours sleep sounds fine to me, but maybe needs to be divided a bit differently - ideally to get her sleeping in a bit later than 5:30? Is she feeding in the night?
I'll tell you what I do. My son is six months old. When he was four months I started him on a routine roughly based on how long he could stay awake before getting tired. I find now that at six months, that is usually about 2/2.5 hrs.
Wakes up at anywhere between 6:45 and 7:30am (I have usually woken him at 7am if still asleep but he has recently dropped 10pm feed so if he sleeps later I have let him for last few days!), has milk feed.
Goes down for a nap about two hours after he wakes - so usually put him down around 9am. He will usually sleep for 45mins to an hour. I will wake him if he is still asleep for much longer than an hour (which he isn't usually). SO say he wakes at 10ish.
At 11am he has milk and then solids (have been weaning him for about 10 days now) - though I will be planning on giving him some solids after breakfast milk in a few weeks and then this 'lunch' will move forward to 11:30/11:45, and he should be able to stay awake a bit longer to eg 12:30.
At about 12/12:15 I put him down again and he has his 'big sleep' which I try to make at least two hours (though sometimes he wakes a bit early), so he is usually ready to get up at 2/2:15 ish.
He will then need another nap to get him through til bath/bedtime, which he will usually have some time after 4pm. No more than an hour here, though can be as short as twenty mins - he really needs this to recharge though.
Then naked time / bath at 6pm, fed and in bed by 7.
Our babes have the same total sleep time but just split differently! Not sure what your nights are like though?