Corrin .....
I would have to agree with the others on both the possibility of it burning at the incision site and also to ask your surgeon.
Depending upon how much of your head is shaved, hair grows on the average of 1/2" per month so even at two months, your hairdresser would have difficulty getting your hair around a perm rod in that area. That being said, if/when your physician gives the OK, if your hairdresser puts Vaseline along the incision line, it should reduce possible irritation at the site.
I had a perm maybe two months before my first surgery. The curl from that perm loosened some post-op but was still enough to be easy to maintain until I could get another one (do not remember for sure, but it was probably three to four months post-op). Before my second surgery, I decided to cut my hair shorter than normal for me and did not have a recent perm. I am leaving it shorter for awhile now (with no perm) ..... mainly because I am not sure I want perm solution around the abutment until after I am sure it is fully healed.
Hope that helps some.
Clarice