My wife is 5'4" and although she could shoot my lttle 308 it bothered her. Went to exactly the same gun (Mohawk 600s) in 6mm and she loves it. A 243 Winchester is about the same. With good shooting those 105 gr bullets are good deer killers. A heavier 243 and a decent recoil pad and maybe a muzzle break and the recoil should be pretty mild.
Good luck.
I was about to suggest a 243 Winchester. There's a number of good deer bullets even in the 85 to 95 grain range.