It has been my personal experience (at her age, too.) that this is a sign of nerves or stress. Do you notice if she is doing this randomly, all the time, etc.? I sometimes to this day attack my nails when I am under the most stressful situation.
At your daughter's age, I found exams to be highly stressful for me (even to this day! LOL~).
The time I was able to stop biting my nails: was when I was on immune-suppressants. I then realized that if I was in between hand washings and if I bit my nails, I risked becoming ill. Even now it happens. As for infections, if she is practicing good washing skills, she should be fine. You could always put an antibacterial cream on her hands at night (or when she is asleep if the nails are particularly bad.) as this will add some moisture and protect the skin. Olive oil works well too (I pick if I have dry skin when I am stressed!)
When she is older, I think she will realize that she wants long nails when her friends have them in school ~ I did! (just watch for cuticle biting.)
Also, I find with my son if I make less of an issue out of things, he responds better! (Go figure!)
As long as she is not able to bite or pick at the toe nails too~ less washing occuring compared to our hands, as there is more bacteria from sweat (hosting the germs, etc. making it the perfect breeding ground), shoes, carpet and ground.
By the way, this works on me: when I have onion, garlic or lemon juice (lemon juice is actually a very good nail conditioner when mixed with warmed oil and soaked on the nails) on my hands, I rarely pick! (too bitter & sour, plus I hate the smell of the onion/ garlic when it is raw!) Of course, if she had bitten the nails down too low, it can sting~ maybe as a prevention in between?
Or get a flavor in 'essence form' from the health food store that she does not like and apply it. Essences are natural and will not harm her if she takes a bite! (I never was stopped with conventional Bitter nail treatments!) I have to keep after myself as I risk infection with my job if I have open sores on my hands (so I apply liquid bandage or super glue if I am out- if I really have to!).
Good luck and I hope she grows out of it! ;)