Time to give info on the MU.
: With her range, speed(not faster than fox), and luma on her side, Dr Mario is gonna have a hard time getting in because of his slow mobility even will pills. Because of her disjoint up-air, Dr Mario has to be careful landing against since his air attacks can't beat her up-air or even reach with drill kick, having slow air speed, and fast falling speed to get out of her juggles. Because of his falling and being alittle heavier than Mario, Rosalina can combo him with down throw(to f-air and to up-air) up-throw to up tile, and other auto cancelled combos from n-air and forward air. Since Doc is slow, she can use her forward tile, down tile, n-air, and jab to stop his appoarches, and run away if luma is dead.
Her off stage can take out Dr Mario with ease because of his low jump heigh(and the jump punch), falling speed, and slow air speed. Her back air can stage spike him if he recovers low, she can use luma to cover his get up and jump on the ledge and Rosalina can punish his roll for a grab, down smash, down tile, and forward smash. Next, her down air which is death for Dr Mario if he gets spiked or knock far by luma's hitbox.
While Dr Mario doesn't have the speed to keep up with Rosalina, he has the damage output, ko options, and moves to knock out luma and kill Rosalina quickly than she can since she's light, tall, and floaty. With his tornado, oos jump punch, back throw, and forward smash, Dr Mario can take luma off stage and focus on putting the hurt on Rosalina. Jab 1 & 2 to jump punch set up might help with taking out luma, but be careful or else, she can punish your landing lag. His power is better and he can early kills against Rosalina such as forward smash, forward air(for a hard read and to the ledge), tornado gimp off stage, and jab 2 to jump punch set up to the ledge(if jab 2 doesn't work, try jab 1 because its more efficient against floaty characters).
While her off stage game is better, Dr Mario can also gimp her too with back air and tornado. While her recovery can reach the ledge more than Doc's, it doesn't have a hitbox and safe to stage spike with back air. While his sex kick can't kill off stage, its useful to launch her farther to force her to use her double jump and use launching star for a easy gimp with Doc. Drill kick and tornado are something to watch out for because he can cover her get up and jump from the ledge. Tornado can also kill her off stage if you can catch her recovery in time and have enough percentage to do so.
Aviod Battlefield and Dreamland because Rosalina can use platforms to her advantage to juggle Doc and give him a hard time getting out of them because of her tall height and his slow mobility.
Customs:
: fast pills and gust cape are your best friend for this match up. Soaring tornado, if you want alittle more height, but be careful recovering with it since its has less height sideways.
:With shooting star bit and teleport star, its harder for Doc because her customs are better, give her options to edgeguard, and to stop his appoarches even more.
I think this MU is at 1.5 best for Rosalina because while Doc has the killpower and damage output to take out Luma and kill Rosalina quickly, Her speed, range, and edgeguarding hurts him more than the mother of stars. This MU will be even harder for Dr Mario than it is for Mario because of his slow mobility both the ground and in the air.
Edit: For customs, maybe 2 or 1.5+ for Rosalina because of Doc's slow mobility and predictable recovery.