Hello,
Yes, sounds like a very good plan! The question is, which beach in Fiji! It is such a beautiful place...
I would personally recommend staying in a local village instead of going the usual backpacker route - for a start you don't end up in a packed dorm or with loads of other tourists...you actually get welcomed as a member of the village, it is like a homestay arrangement, and it is probably one of the cheapest options in the whole of fiji.
info on the homestay options (along with bus info, taxis, maps, weather, what to take etc) is at www.fijibure.com - unfortunately there are not really many hotels in fiji that are NOT expensive, but if you stay with the locals you end up living like you would on a resort, except with hardly any other tourists!
Good luck, and i hope you have a great time!