Fiji is an extremely safe country to travel to. The major bugbear is mosquitos; these can carry dengue fever and elephantiasis, though dengue fever is only active during the months of November to April. Make sure you cover up at dawn and dusk and use insect repellent. You have been warned.
Fiji, like most of the South Pacific, can have intense solar radiation that can cause severe skin-burns in a short amount of time. Be sure to use hats, sunglasses and liberal amounts of high-SPF value sunblock on all exposed skin (including ears, noses and tops-of-feet) when out in the sun. Also, if you're diving or snorkelling, then it's even more important you do it as the winds / water will mask the heat of the sun. Rash vest it up.
Even though the local water is safe, it's always recommend to either buy bottled water, to filter water or to boil it. You don't want to become ill on your gap year by a water-borne illness.
All medical care in the main tourist destinations is very good, though if you get off the beaten track then it's harder to come by.
In case of an emergency police number is 917, and fire and ambulance is 911. The main hospital is located in Suva.