LOL. Is $5 okay to start? She'll think you're the most generous person on the planet!!!! I'd discuss it with her Mom first to ask if that's too much/too little depending on what they've taught her regarding money and financial responsibility thus far.
As for asking the Mom to babysitt and what to pay: just ask. Say, "Listen, I don't know whether or not I should pay you in money or a likewise night off so you can get out in an adult style. What would you be more comfortable with?" My parents traded babysitting nights with a set of friends, no money.
*hugs*