I went to Fiji in Spring 09 while studying in New Zealand. One thing I can tell you is that the climate is very warm and very humid, so you'll want some lightweight wicking layers (like Capilene 1) if you're going to be hiking a lot. I mostly bummed around when I was there, but I did go hiking a few times and it was REALLY muddy. It's the kind of mud that is just wet enough to be pliable, and your leg sinks halfway into the ground. I'm not sure what the best footwear solution would be in this case. Possibly something like Chacos would work best? Flip-flops would get sucked right off your foot and any sort of hiking shoes are going to be encased in mud.
Another consideration is water treatment. They do recommend that you drink bottled water there if you aren't local, but I ended up accidentally drinking quite a bit of "local" water (in the form of kava-kava...haha) and my stomach felt a little shaky for a week or so. I'm going to step aside and let someone else recommend the best water treatment (filter, AquaMira, SteriPen). Keep in mind that there are a lot of livestock in the area, close to the water sources.
I didn't find the bugs to be that bad when I was there, and they don't make you get malaria shots or anything before you go. But it would be nice to have a lightweight bug headnet, a rain jacket, bug spray, and maybe some lightweight wind pants for protection from bugs.
As for backpacks...maybe check out the GoLite Jam? You can get them for $90 each from Golite.com by entering in coupon code: BSF10. They also make women's specific sizes which is nice, and the material would hold up for world-traveling. It's a nice lightweight pack for roughly 25 lb loads, which is plenty considering how little gear and warm clothing you need to backpack around Fiji. I guess I'm not too clear on what sort of backpacking trails there would be in Fiji, both of the "big" islands are still quite small.
In any case, you will have a blast in Fiji. The people are genuinely the friendliest in the world. We stayed in a resort/hostel hybrid sort of thing. The bunks were cheap ($20/night), and they had private cabins too. They employed people from the local village, so I think a lot of the money stays local (hopefully). The staff there will be your best friends by the end of it, and they were always planning activities (visiting the local school--very rewarding, coconut bowling, horseback riding, dancing, movies, snorkeling, pretty much anything you can think of) and getting people involved. It was a younger crowd (the typical 'backpacker/hosteller' crowd you'd find almost everywhere, but there were young couples and even some older folks as well. It was an awesome experience (and it only cost me $400 for round trip airfare from NZ, plus the week's stay in Fiji). Maybe you would consider doing something similar, instead of staying in one of the "big name" resorts. It really depends on your preferences though.
Speaking of that...if you want to do some world class backpacking, maybe schedule a small trip to NZ while you're on that side of the globe. You won't be disappointed, it's legendary (so is Fiji, though).
Sorry for the rambling post. Maybe giving some more specifics on what type of backpacking you will be doing, as well as your backpacking experience, will help people give better advice.