When I got my Dremel 2 years ago, I also got the 220 piece accessory kit that had the circle cutter but I didn't use it until recently and then on a 1x10 pine board (shelf board type). I didn't drill a pilot hole all the way through since the circle is what I wanted, not to cut the hole OUT.
I found that I needed to put a nail type hole/dent in the board to help the cutter stay in the right place and also circle the space several times getting progressivly deeper. While this was going on, I kept one hand on the pivot point to ensure that the point didn't wobble. My other hand held the tool to guide it. The board was on a surface that supported it and my hands kept it steady. Although the circle cutter tool holder has a shroud around the cutter, this also encouraged me to keep my fingers out!
When the circle was cut out, I used a 1/3 sheet sander with 60 grit paper in it to smooth out the edges and put a small radius on the edges.
I agree that you should be cautious about breathing fumes that may come off the glue with MDF. My concern is that it could really build up on the cutter. In any case the work should be done outside or some place you can clean up easily since it really generated the sawdust!