Emma, if it were me, I would let her sleep and not wake her and put her down maybe 30mins earlier for the night. I did something very similar with Jasmine recently (both girls are on/off sick for 2 months now
) and she was also very tired as early as 9am. I tried to hold her off until 11am and then let her have a nap as long as she wanted. Instead of 7pm bedtime, I put her down for the night around 6.30pm.
See how you go.. but I agree with you in that one early morning nap shouldn't do much harm
I hope she is feeling better soon