What an even-handed request, Linda!
Tortie is absent from most dictionaries, but it is listed in the Shorter Oxford. And it is certainly in use, on lots of cat-related websites, and in books, too. So it makes the grade.
Rottie, on the other hand, is not in the Oxford, or in any other dictionary that I looked at. Yet it seems to be used just about as widely as
tortie. Perhaps more so, in fact: there are more results for a Google search on
rottie than on
tortie. Also, there are no occurrences of
tortie in the
British National Corpus, but 9 for
rottie (although they all come from the same source:
Dogs Today).
The word
rottie is often written with a capital
R, as is the full name,
rottweiler. Presumably this is in recognition of the word's origin, from the town of Rottweil. However, I think the words are written often enough in all lower-case that this issue should not be an obstacle to us allowing
rottie.
So, the only real barrier to accepting
rottie is the lack of dictionary recognition. But in this case, I'm willing to go against the dictionaries -
rottie certainly is a word, and quite a widely-used one, and no doubt the dictionaries will catch on to it eventually.
So I'll be even-handed too, and allow both words.