An even worse recovery than Mario's up b so it's even easier to gimp.(Keep in mind that Dr Mario has more kill power though.)
Punish the double jump to leave him with only his lackluster Up+B
Unless you're playing a super heavy hitter, Dr Mario will be at an advantage with most trades. Don't opt to trade blows unless he's at kill% or near off-stage.
Try to pick stages with higher platforms, or no platforms at all, that way d-throw->downB no longer works for Doc as a true low% combo.