Thank you for your query.
Though you have mentioned that the red dots come and go on your daughter you have not mentioned the duration for which these dots last. As they do not hurt her I suggest that you should discuss with your doctor and request that the following investigations be performed:
1. Hess test also known as tourniquet test.
2. Haemogram especially platelet count
3. Bleeding profile.
The clinical examination and/or investigations should lead you to some diagnosis and remedy of the problem.
I hope I have answered your query to your satisfaction.
Wishing your daughter all the best.