Unless your daughter's life depended on skating, I would not advise her to skate when she is ill for two main reasons:
1. Skating is a strenuous physical activity, despite it seeming so effortless. There's a reason you don't feel good when you're sick -- your body needs time to recover, and strenuous physical activity will stress your body some more. Sure, you can probably skate well for 4-5 minutes, but as you have seen, that translates to a longer recovery time.
2. You can infect other kids at the rink.
A general rule of thumb is that mild exercise is okay if your symptoms are all "above the neck" (e.g. runny nose), and any exercise is not when symptoms are "below the neck" (e.g. chest congestion, fever). Here's the full article from the Mayo Clinic:
http://www.mayoclinic.com/health/exercise/AN01097Coaches should be careful in giving "medical" clearance for their students to skate. I remember one coach from my old rink who wrote a letter online to an MD, asking advice for her student who had a broken (or otherwise injured) ankle. The student was wearing a cast and the coach wanted her to skate! Of course the MD advised against it -- I can only hope that the coach followed the MD's advice.