Well, the contact pattern between the ring and pinion is supposed to be in the middle of the teeth, so most of that damage shouldn't hurt, but that one tooth is iffy. I had a hot rod that ground up the spider gears into powder, and the ring gear had damaged corners. I cleaned out the axle, threw in some junkyard spiders, and kept on driving. After about a year the pinion bearing gave out in a bad way, totaling the axle.
I totally agree with foundrydude. Personally, I would clean out the axle real good and avoid burnouts. Drive it till it breaks. Meantime, go to a you pull it yard and get another axle cheap, overhaul it, and have it on standby.
My cylinder head overhaul: http://www.jeepforum.com/forum/f13/cylinder-head-r-r-picture-heavy-1348138/
My transmission overhaul: http://www.jeepforum.com/forum/f13/how-change-transmission-electronics-1560948/