E.D.
Actually I think it does sound steep. Around here it would be $30 - 45/ 45 min. or hour.
I grew up learning violin in the Suzuki method from age 4-12 at which age I "quit for good". At 18 I picked up a violin and was exposed to new ranges of music. I fell in love with playing again. Having formal training at a young age helped me get to advance quickly.
On the other hand, I have friends who taught themselves to play guitar/accordion/violin/cello/drums/you name it in their teenage years who's talent far surpasses my own abilities and passions.
Your daughter sounds passionate about music! What a great gift you are giving her. Technique and method will really help her, but your support and her creativity will be much more helpful.
If you can't afford her teacher, I suggest you look for a really inspired musician to teach her in the Suzuki fashion: by ear until she is develop mentally ready to learn sheet music.
When she 'composes' her own music or just seems to melt into her music...encourage that. She will learn to love her talent.