At 13 I was doing several things to earn money - here are some that might interest you:
petsit (which I see you are already going to be doing)
Key thing, let it be known that you are anxious to work to earn money. If you attend a church, get the word out (church is a hotbed of gossip which can be used to your advantage in passing the word around, lol) that you are looking for work. When offered a job, don't turn it down unless it is something you know you can't do or is dangerous to you -- it may not be the ideal job you wanted, but it's a job and your willingness to do that job will open doors to more, refusing will close doors....not saying you can't say no, just saying don't be too picky about what you will do. A lot of the suggestions I might have will depend on the area you live in as some ideas are simply not feasible for certain locations - for various reasons. Don't give your actual location if you aren't comfortable - just answer if you are in a rural area or large metropolitan or the 'burbs.