Hi Sophsmum,
My son has a humapen luxura by Lilly, which does 1/2 units, his is for use with humalog 3ml cartridges. I don't know of any basal insulins that come in cartridge form as ours have always been prefilled disposable pens. Hope this is of some help, or i would do as Ken suggests and give a higher carb snack before bedtime. If she usually has eg 20g carbs before bed try adding a glass of milk or a larger portion. I understand how difficult it is, i have a 10yr old son, sometimes before bed their just not hungry or the opposite as with my son, he'll eat a happily eat the contents of the fridge.
Hope this is of some help.
Take care and good luck,
Suzi x