We can only guess and make suggestions, but if I had that result, I'd look at my pre-meal BS; my mealtime insulin dose (timing and amount); and my basal. My hunch is one or more of those is causing the problem or certainly making it a lot worse.
You're reporting high sugars, and there are a lot of them (the odd one isn't abnormal). I know you said your daughter's basal had been reduced because of hypos, but perhaps - and this is just something to,explore with her team - you could increase the basal fractionally when you get the CGM so you can monitor her closely. I'd also ask about splitting the basal dose - to two injections a day. Many people on Levemir find that helps control a lot.
Prebolusing is hard with a child, but it can make a big difference to any spikes - an almost unbelievably difference. I'd also suggest asking to,try Humalog instead of Novorapid, as many people find it acts slightly faster.
Once you get the basal dose fairly sorted, you can then assess, with your daughter's team, whether her mealtime insulin to carbs ratios need to be changed.
If you approach this systematically, you can make improvements, I'm positive.
Note - when you say she went up to 13.5, how long after the meal was that?