In theory the levemir is only there as background coverage and should not be used to cover snacks, however, if the dose is too high then a larger snack will be needed prior to bed and probably snacks between meals as well. You have to remember though, the blood will go up relatively quickly, but take several hours to come back down to the desired level in the morning, resulting in higher blood levels through out the night, not an ideal situation. You then may as well be on the mixed insulins, we are not seen to be as effective since they don't bring the blood down as quickly as basal/ bolus regime.
If your daughter is like my kids, they sleep about 11 - 12 hours, so her blood sugar levels would be higher than you would like for a long period.
We have also had this problem of snacks at night with our kids, as they are quite young, they like something before bed, but we don't like giving novorapid before bed encase they hypo. We now only give them a small snack ie 5g of carb if their blood sugars prior to bed time are lower than 7mmol. We try and compensate with things like popcorn, crackers and cheese, sugar free jellies or sugar free ice-pops. This issue has always posed a problem for us too, we also have the added problem when one can have a small carb snack but the other one can't!