How old is she Harry?
My 6 year old daughter is T1 too, diagnosed 16 months ago, but we only had to use the injections for the first 5-6 months before she was put on an insulin pump (Omnipod). The pump is so much better than injections, you can give different base levels of insulin (equivalent to the Levemir) for different times of the day and night, and you can different base settings for days when she has PE etc, then when you give her insulin at meal times for the amount of carbs consumed, it knows how much insulin she still has on board.
Great piece of kit, would she benefit from that?
PS, i can sympathise with the tiredness, 56 mile round trip commute on bike last night, then home to change daughters insulin pump (done every 3 days), feed and bath her, the cook tea for my wife home from shift, then up every two hours to daughter in night as she is ill at the moment! Doesn’t get any easier does it!?