Maybe some binoculars at that age.These here are not toys,but are close to half your budget.They are only 10.2 ounces and they have an unparalleled close focus of 18 inches.They would fit her hands and they are pretty tough.She could study things from the moon to her toenails and everything in between,birds,butterflies,leaves and such.
They are rated by adults 4.8 stars out of 5 at Amazon and binoculars.com and 5 out of 5 at Eagle Optics.I got mine there and many others in the $1000/$1700 range without the first problem.They will also answer any questions you might have about any optics.
http://www.eagleoptics.com/binoculars/pentax/pentax-papilio-6-5x21-binocular