You can afford a place making $3000 a month. It's hard when rent is half your income, but I've lived in that situation so I know it is possible.

In many towns there is a low income housing list. You guys can sign up for it. It may be a long wait, but eventually they'll call you for an affordable apartment. And some places do take dogs. You can also get assistance with your electric bill based on your income. There are many resources available. Don't rule out getting an apartment.