What questions should I ask our doctor concerning our daughter's repeated illnesses?

My daughter is 7 and attending first grade. Since the beginning of kindergarten she’s been ill at least once a month during the school year. Usually a high fever of 102–104F that lasts a few days (at least), accompanied with a cough, sometimes a headache and vomiting.

Once a month seems extreme to me so I asked our doctor what could be wrong. We heard everything from “It’s that time of year” to “It could be allergies, have her take claritin”.

I have a gut feeling something else is wrong. My sons were never ill this much. A high fever every month during the school year for two years now?

We are looking for a new doctor. Are there any tests that I should ask for? Is it common for a young child to get ill like this so often? I’m so frustrated with our doctor’s advice because it isn’t helping. :(