I started my period at 10 years old, back in 1987. It is actually very common/average to start at that age, nowadays. She is not too young to take care of her body properly, she is toilet trained, takes her own baths, gets dressed, does her hair, Right? No offense meant, BUT this should not be an optional thing, it is part of proper personal hygiene and growing up, she doesn't get away with gong to school without brushing her teeth or hair, does she - think of this the same way.
Her mom (or maybe it would be less embarrasing for the girl if an aunt or cousin or older friend) needs to tell her that toilet paper rolled up is just going to be a probelm/embarrassment sometime! Explain her how periods can suddenly get heavier as she grows, and she could leak through, or the TP could wiggle over and fall out of the leg of her undies and pants - talk about mortifying! Maybe tell her a personal story about a mishap with period and say how if she just uses pads, keeps some in her locker/purse/backpack, she can be prepared!
I can understand not wanting to use the granny pads like my mom gave me - like the postpartum ones from the hospital, or even tampons, they are tricky, and putting something inside can gross a girl out that young, not to mention hurt, even the slim ones. My mom bought th ehuge Kotex in the cardboard box back then, they were horrible, and I got so fed up with them, I asked her for some Always thins, she said if I wanted somehting "Fancy" i would have to buy it myself - so I took my allowance and did - and then SHE started using them, after taking one of mine!!!! So maybe she thinks whatever Mom uses is what she has to use and doesn't realize there are tiny, slim, thin, flexible versions out there, or is afraid she will have to go along to buy them, BUT there are so many better choices out there now for pads, they stick great and stay in place, they are so thin they almost feel like nothing but undies, and they make them so absorbant, she wouldn't have to change very often.
Someone should go out and buy her a variety of thin pads of different types/brands, and just discretely make them available to her. Like others said in a non-descript box in the bathroom or inside a drawer or basket, so not everyone sees them. Also, maybe buy her a purse or small makeup bag (to zip them in inside of her locker or backpack) to use at school at that time of the month to keep her own stuff in, so no-one else has to see her carying a pad or tampon to the bathroom.
Maybe her grandma or great grandma should explain to her how very nice and discrete and convienient these new products are, compared with wadded up rags, or the original disposables that had to be safety-pinned onto a "belt" to wear them! Here is actually a website dedicated to the history of menstrual products - we've come a long way baby!
Good Luck!
Jessie