I had this "rash" as a 2nd grader. At the time, our Dr. in Nashville, TN sent us to an oncologist at Vanderbilt University to investigate the cause. Mine came on pretty quickly, but the smaller "spots" hadn't been so noticeable, but large bruises on my legs appeared (for no reason) and I got a bloody nose that wouldn't stop for a very long time. This led to my dad taking me to the ER ... followed by frequent dr. visits for quite some time.
The deal is, this would be caused by a low platelet count. After numerous blood tests - for me, they couldn't even find my platelets ... People are to have over 150,000. Finally, they found approx. 13,000 in my blood. Because platelets are produced in the bone marrow, the next step was to test my bone marrow to see what the underlying problem was. Thankfully, it wasn't anything long term and serious. There are some that are... but I don't want to cause you to worry about anything ... just do what you can to learn about what is going on with your precious girl and causes/tests. I will forewarn you that a bone marrow test is not comfortable or easy to watch... but I managed to endure it at 7 yrs old (Of course, I still remember the experience and I'm now 35.) Most of what i remember is the fear of what was going to happen, that there was pain, that my Daddy held my hand through it all. They might do things differently nowadays.
I haven't read the entire sit of the link I'm sending you ... but it is just one medical source online's description of the petteciae (I always thought "petuchiae") ... causes, symptoms, and so on.
http://www.mayoclinic.com/health/thrombocytopenia/DS00691...
Lord bless you and I'll be praying for your daughter!
p.s. Everyone here is so kind to offer input. Please know that pettechiae is not a skin issue, so a dermatologist cannot do anything. As adults, we might develop dots all over our skin for various reasons ... but the condition A. is describing is not in the skin.... it is dealing with platelets...which is the actual definition of what the Drs. are stating. Please forgive me for being so bold. I know everyone is trying to help!!!