The frog catching minigame may seem like a stupid waste of time -- but it can actually be a source of some good items and new weapons for Quina, plus the number of frogs Quina eats will power up the "Frog Drop" spell. Here are the rewards:

2 frogs: Ore Stone
5 frogs: Ether
9 frogs: Silk Robe
15 frogs: Elixir
23 frogs: Silver Fork
33 frogs: Bistro Fork
99 frogs: Quina's Master appears and fights you; just use standard attack/heal techniques and be around level 40. You'll get the Gourmet Fork for winning.