I used to have to "pay rent" to my parent's, when I worked -- $20/week which my dad turned around and gave me towards a car after I moved out (what a nice guy

) -- but is she clear you want to move out and are you old enough to do so?? Let her know your goal and if she needs you to contribute, work out a reasonable amount to give her and that's it.
However, I do believe you should probably contribute to "your stuff" -- clothes, etc. I had to pay my own car insurance and up keep and my clothes/stuff for work.
Good luck.