Middle easterner here who was your daughter 20 years ago. Here's what you need to know about female hair care:

See, shaving makes hair grow thinner and waxing makes it grow thinner. Thus, in the long-term, it is better to wax hair. However, for a lot of ethnic girls, hair thins and lightens naturally as you grow up. If leg and arm hair is the main problem, then teach her to shave. Get shaving gel and SINGLE blade disposable razors for her. For the toes, I suggest teaching her to wax them off since I doubt she will ever want to have hair there. Shaving is much more manageable everyday for a young girl as opposed to waxing large areas like arms and legs. Plus, you don't know if her hair will thin out. Maybe when she gets older she will want to consider waxing? For the eyebrows, take her to a solon and have them waxed. They can clean them up for about $10-12.

LASTLY, I just want to add you are an awesome dad for addressing this. I grew up in a predominantly Polish/Irish neighborhood, while having a unibrow, arm-hair, leg hair, a mustache, and hair on my toes. I was made fun of SO MUCH for this, but my parents were conservative and forbid me from shaving/waxing, etc. By 11 years old, I had my moment of rebellion by shaving almost everything off. From then on, I had to teach myself everything just to keep my self-esteem up. You are actively doing this for your daughter. God bless fathers like you.