7 yrs living in Doha, there is no piano rental as such. I think you will have to buy for the last resort. Get the digital clavinova if you want to cut the cost.

My son goes to an Indian lady living in musheireb. He started from zero and it seems like it. Drop me a PM and i will give you her mobile number.

Or if she is more serious go to International Music Centre behind lulu hypermarket, they do Royal exam.