Last night, apparently having a passing feeling of pique over how people put Rose Tyler in, like, Every Other Thing David Tennant's Ever Done, I facetiously wondered aloud, "How come it's never Rose from the Golden Girls, huh?" Then it occurred to me to think, fandom being what it is, that oh no, somebody probably had done just that. But the closest I could find on either FFN or AO3 was someone who apparently enjoyed making Leonard McCoy boink every other character they could think of, to judge from the tags, and this included Rose Nylund; so, that's Rose and a doctor, but not the Doctor. Alas.
(Not that I would actually want to read the genuine article, mind. Eep.)