I'm a life-long nail biter, and my Mum and my Gran before me. I do believe it's behaviour I've inherited but also learned.
My DH also bites his nails and now I've noticed DD (age 2.6) has just started. 
I've spent 30-odd years looking for a way to stop myself and have had most success by giving myself regular manicures. If my nails look nice, I'm proud of them and am less inclined to nibble.
Can your DD wear nail polish to school?
If you can afford it, why not take her for a professional manicure as a treat, so she knows how to care for her nails? Then, also if you can afford it, buy her some nice (OPI or Jessica) polish, nail files, buffer, clippers, etc. Or a stack of cheap 'n' cheerful polish (Rimmel).
What about a small manicure kit to keep in her school bag/pocket? I find that having an emery board and a small pair of tweezers/clippers in my handbag means I don't chew on scrag ends.
It might also help to identify when she chews them. Is it in school classes? Could she do something simple like sit on her hands or find something else to do with her hands instead of nibble? For me it's when I'm driving the car (in traffic or at lights), but I'm aware of it and try to stop myself.
I don't think that false nails will help, sorry!