[Kalimac]

The fact that it's Gimli who's worried makes me inclined to believe that he was just being nervous; there's the previously-mentioned fact that Dwarves (like hobbits) don't seem to be big fans of water travel, and there's also the fact that Gimli is naturally inclined to mistrust Elves; his "Welcome to Lorien" was probably a rather unnerving experience. Yes, he did fall in love with Galadriel, but that doesn't mean he's going to shake all his convictions about the innate slipperiness of Elvish promises all in an instant (it takes him till TTT, after all, before he starts getting truly friendly with Legolas). Probably the only way he'd be inclined to have faith in the boats is if he was told that Galadriel made them personally.