Just to give you more idea. I take my 24hour Lantus at around 3PM daily. Although it is meant to last consistently for 24 hours, most will find that a 'spike' happens for the first few hours after taking it, and it starts to 'tail out' towards the end of the 24 hour period. I find 3PM to be a good time as it's in-between meal times, meaning that I remove the variable of having to administer fast acting insulin or food at the same time.
I became Type 1 when I was 4 (I'm now 23). My mum used to mess my levels up all the time, and while that wasn't good, at least as a child I had a large ability to 'heal' my body without doing too much damage.
If you want to stop night time highs, test her sugars maybe an hour before bedtime, that way you can adjust her levels (with fast acting insulin or food) without panicing about her going to sleep right away. It may even be an idea to wake her during the night and test, just until you get it right.
You'll get it right in the end, and you're doing the right thing by increasing the dosage slowly (you don't want to give your daughter night time hypos).
Remember that everyone is individual and what might work for one diabetic might not work for another.
Stick with it, and good luck.
