Just chiming in to third the vote for food grade DE. This stuff works amazingly well. I only had cause to use once, well over 10 years ago, but it worked wonderfully for me and very quickly. (I noticed a significant difference on the very first day of use with no need to reapply.)
For carpet use: we had a tight knit Berber-type carpet. I sprinkled generously, then let it sit for as long as possible before vacuuming (ie: 4-5 hours). (I didn't want to leave it because it's a VERY very fine powder and very easily tracked/transferred to EVERYTHING. Even with extensive vacuuming, we were still getting residue from it months later. Nothing awful, a fine layer of it would just appear over items near to the floor over time.)
Caveat emptor, back when I initially heard of it and used it, caution was given regarding inhalation of the DE. The very properties that make it so effective in slicing through the exoskeletons of bugs, can make it dangerous to inhale as it will work in the exact same manner on our lungs.
To be on the safe side, I wore goggles and a face mask during clean up as the friction of the vacuum over the carpet created a bit of a dust up. Nothing like a smoke cloud or anything, just enough to make me want to be better safe than sorry. (We had a VERY small apartment back then, though, which I think contributed to it being a bit messier than it otherwise would have been.) It's safe to ingest, but I had read that breathing it in can harmful. I'm not sure if that has remained true over time or if that has since been disputed. It's something to consider, though.
DE is extremely cost effective, much much safer for everyone involved and so much easier and simpler than calling an exterminator.
I'm not sure it's necessary to treat the yard if your cat isn't an outdoor cat. If needed, you can just work some DE into her fur to keep her flea free in the future. Given how often cats clean themselves, daily application may be necessary, but I bet she would love the extra attention.
(You can treat the yard, as well, with DE, though, if you are so inclined. You just need to make sure to reapply after rainfall.)