Drilling a 1-1/8" hole in plastic with a Dremel
While this can be done with a Dremel (I've done it), you'll get a much better result picking up a paddle bit or hole saw and a hand drill. If the exactness of 1.125" is not particularly required, you can go with the dremel, but if you need exactly that hole size (say, you're trying to minimize possible air leaks in something) I'd say you need a drill.

Edit: I just realized you're using a dremel on plastic -- This will lead to bits of high static plastic everywhere. In addition to that, whatever you cut will not have clean cuts, there will be melted plastic all the way around the edge. I won't say this isn't an irreparable situation, but getting a drill probably is your best bet.

Aside from that, almost any home based project will be 100x easier with a drill. It's one of the few tools even the least DIY people should have around the house.