My wee boy was diagnosed at 4 and we started on the pump 18 months later. Is it better? Yes, but more difficult, and it isn't a cure for the issue you are facing i'm afraid.You're still bolusing for meals in essentially the same way so the insulin is likely through before they start refusing food. You could put on a lower temporary basal to compensate, but she's likely to be on such a low hourly rate that it won't make enough of an impact. Using a dual wave could be an option, but it takes quite a bit of experimentation to get that right.
What i'm saying is that the pump is great but i wouldn't be in a rush to get one, and honestly knowing what i know now i wouldn't have taken one in the early days. Definitely try bolusing after, that worked well for us, and if you can, involving her choosing her food - what 'counts' and what doesn't. It helped my son focus on eating the food that we bolus for, and if he ignored the carb free stuff then so be it.