When you arrive in the Dragon isles & get off the boat, there’s a fishing trainer along the shore. Take advantage of that because you won’t see another one for a while.
Dragon Isles fishing levels up pretty quickly. The first 10-15 casts I was getting 1 point per cast, then it settled down to one point every other cast & it stayed that way to 100. Took me 189 casts to hit the skill cap.
There’s a river running south-east from Uktulut Backwater in The Waking Shores; get up on the ledge on the south side of that river & there’s some nice quiet pools to fish in with no hostile mobs around. The one at 58.3, 47 worked out pretty well for me but there are a few others nearby that look just as nice. (BTW, if you’re in the area there’s a rare mob that sometimes spawns in the hot spring northwest of there; it wasn’t there the first couple times I went through but eventually showed up. Dropped a Drakewatcher Manuscript.)
I fished up one Copper Coin of the Isles. Apparently there are also Silver & Gold coins, and you want to save those until you fish up a Rusted Coin which starts a quest leading you to a vendor who will take those coins in trade. (Edit: I just noticed I have the Rusted Coin quest, so maybe I got that when I fished up the Copper Coin? I’m not sure now.)