Which Neder (vow/oath) can the father nullify?
The vows that cause her physical pain (inui nefesh), and those that affect between him and her (beino levainah)rosh, ritva, Ran, nimmukei yosef and tosfos)
Alternatively Any neder whatsoever (Rambam hilchos Nedarim 12,1 see kesef mishna there).
Ussually the father owns the money (her work payment and findings belong to her father Nidda 47a) , this is between him and her since he would pay up in order for her to fulfil her neder as she doesn't own any money yet. So as long as he is mefer (nullifies) ביום שמעו - on the day he hears the neder (numbers 30,6) her neder is nulified according to everyone.
If she has enough money from her own pocket to give to charity e.g she inherited from her deceased divorced mother or received a present on condition her father cannot benefit, then this is nothing to do with her father,only the Rambam would allow to Mefer her Neder.
What happens when she goes out of her fathers reshus (Domain) e.g marriage/full maturity?
According to Ran, Rosh, tosfos and nimukei yosef ritva then the neder comes back on to her and she has to now fulfill it . this is because SA YD, 234,55: ודברים שבינו לבינה אין ההתרה אלא לעצמו כל זמן שיש לו בו תועלת דהיינו כל זמן שהיא תחתיו - Matters between her and him there is nullification of the vow only when he has a reason i.e it affects him. That is only whilst she is in his domain.
However according to the Rambam the vow is completely nullified for ever as the father has complete power over whatever neder she says even if it doesn't affect him whatsoever.