You should hair removal ASAP, but with that being said, a couple months won't make a huge difference. I started laser about 2-3 weeks after starting hormones I think it was.
The deal I got was from Pure Med Spa (might possibly be a chain in your area?). 12 sessions of laser for my entire body, face to toes and everything in between, for ~$1100. Not bad considering 5 years ago I paid for 6 sessions of laser on just my crotch for about $900, which didn't take! The technology has come a long ways though and after 2 sessions I'm already seeing better results. Could be the HRT helping too though, but I don't care, whatever gets it done!