Fireplaces, Heating Stoves, Flues and Chimneys - Advice on replacing fireplace doors

We've got a brick fireplace in good condition, but with a crummy overlapping fireplace door. It's battered, covered in soot and doesn't stay in place. So we're going to replace it.

Rather than go with a fireplace door that just hangs on with a couple of pressure-mount screws, I'd like to get something that attaches to the actual masonry. I'm hoping to even do it myself. So my questions are:

a) How do I tell if a set of fireplace doors can be screwed directly into the brick?
b) How risky and/or complicated is it to do? From what I've read, it shouldn't involve too many tools.
c) Should I have the work inspected by a chimneysweep or other professional if I do it myself?

Thanks for any advice! :D