A trailer is going to add a significant amount of weight and drag, and you don't really need that much cargo space for that short a trip. Racks and panniers will work better, and will handle a fair amount of your shopping as well.

That said, trailers can be handy for larger errands. The Burley looks nice, but if you're on a tight budget I'd watch the local classifieds for a used child trailer. With a bit of patience, you should be able to find something for under $50 (although your chances would be better in the fall). You can either use it as-is (if you're mostly hauling things like groceries), or strip it down and bolt a sheet of plywood to the frame to make it a flatbed. You can find a number of examples over in the utility forum.