I've struggled with the same thing and have just recently got it under control. Theres a few things to consider here:
The basal - From my experience, the fact that her numbers are fine when she wakes up after sleeping in (did I understand this properly?) does not mean her basal is correct. The morning basal really needs to cover someones dawn phenomenon, which doesn't usually occur until someone actually wakes up. This is why, on weekends when I sleep in, I don't start my basal increase to cover the dawn phenomenon until later. I think you should conduct a basal test (have her not eat breakfast, and monitor BG to see if it rises without any carb intake) on an actual school day. This will account for the stress of waking up for school, which could play a role, and also waking up at her usual time. I understand she probably wont appreciate it, but it's a good way to rule this out.
The GI - Personally, I definitely can't eat most toast, waffles, or cereals for breakfast without spiking similar to your daughter. What has worked for me is switching from whole grain bread, which is medium GI, to pumpernickel rye bread, which is low GI. I also have it with natural peanut butter, slowing digestion without adding sugar (processed peanut butter can actually have a decent amount of sugar). Besides toast I also have a stir-fry with beans, which works great, but obviously I don't know if that's practical for you and your daughter.
The I:C ratio - after the BG spiking, does her sugar eventually return back to normal without any additional insulin? If not, there is an insulin deficit, and this could either be from an insufficient basal rate or I:C ratio. If she does return back to a healthy BG without extra insulin, it sounds like the food she is eating is too high GI, but if not, more insulin in the form of basal, bolus, or both is needed. Once you know the basal is set properly, you can conduct a bolus test by having her eat an amount of carb that you've made sure to count precisely. Wait until all of the bolus is out of her system, and then do the math to figure out the correct I:C ratio. For example, if she was 180 after the breakfast bolus had left her system (i.e. 5 hours after breakfast), and her correction factor is, say, 54 mg/dl per unit of insulin, you can assume she needed 1 more unit for breakfast (meaning she would finish at 126 mg/dl rather than 180). If her original I:C ratio was 1 unit for every 20 grams, and she had 60 grams for breakfast (meaning you would have bolused 3 units), you can calculate her new I:C ratio as 4 units:60 grams of carbs, or, 1 unit : 15 g carb.
I really hope this helps, and please ask if me if you have any questions about what I've written.