it might be seasonal but i don't think it would be a niche market. you'd just have to make the right people aware.
i'm like Santa, very private, can't share my bathroom, but i know that's quite rare (there are more of us on r u than i've met anywhere else) and loads of people have animals they 'can't go away' because it means leaving them. don't be put off this one, di, it could be a useful part of your 'portfolio of careers' that we're all supposed to have nowadays.
people like someone in their house while they're away, too. it keeps out the opportunist burglars. if you model yourself as 'auntie di' they can all tell their neighbours their auntie di will be staying while they're away.
its like a doula for animal keepers really. you should advertise abroad too.