Babysitter or not? Please help

I’m not sure if I should find a babysitter or not.. I have to take my husband’s childhood cat to the vets and probably put her down.. we think she is dying, since she doesn’t move, won’t eat and losing fur and is 16-17years old.. His cat isn’t a kids cat either and lives with my brother in law so she isn’t stressed by my two kids, and we didn’t want to separate her from the cat she grew up with(they got them together).. my daughter hasn’t been to a babysitter and she’ll be 6months soon.. I’m not sure if I should be taking her with me on Friday.. my oldest will be in school.: I’ll be by myself since my husband works.. should I get a sitter to take his cat in or not? I never put an animal down before