Rats will be associated as food-stealing pests rather than the way they would be in a city (diseased baby-eaters or whatever), right?
I'm assuming that the idea of a pet rat would be as alien and unpopular as the idea of a pet slug would be today. I want her to have to hide the rat, but I also want to be able to predict the reaction when it's found. Kill it on sight? Tell the girl to let it go?
Obviously, next to impossible to Google.
Also, if there is any historical data on attitudes towards rats at the time and/or references about them being pets (slim chance, but still), I'd greatly appreciate links!