Carbon rod can be broken while fishing for moat in the three main towns, rusty subligars don't agree with them. >< It's safe to use carbon w/paste in Rabao if you can get there, and you'll only have moat carp and sandfish biting on insect paste there. I used to use a carbon rod in the small pond in la thaine, never broke one there, but you'll catch bass in addition to moats there. I believe rolanberry fields is also carbon & paste friendly, but you'll likely want a 50+ job to handle some of the mobs you can catch there. Knightswell is pretty good for moat, but arrowwood logs can break mithran rods there even, not sure about the halcyon, but pretty sure they can break hume as well.
Personally, when I fish for moat now to work on my lu shang quest, I use a hume rod and lil worms more often than not for bait. I seem to find the hume rod lowers their stamina more quickly, and once your skill raises high enough, I tend to catch as many moats with worms as I do with the more expensive paste, especially if you can't make your own.
Check over in the Trade Skill Forum, there should be a sticky about the various crafts with links to some guides, including fishing if it's something you want to pursue very far. ^^