Yup, he'll be bringing his axe. And no, "axe" isn't just a metaphor for his allegiance; he will definitely be bringing a lot of axes.
Gimli is the most lovable kind of stubborn. At first he might come off as a little dense when he tries to crush the Ring with his axe—which probably wasn't the best idea even if it was just a normal hunk of metal. And yes, maybe he also comes off as a bit racist when he refuses to see the Ring taken in the hands of an elf, but by the time Fellowship has come to a close, Gimli is one of the most endearing characters.
Gimli is cheerful when the trip begins, urging the hobbits to take down Boromir as he trains them. He's distraught by the death of his cousin, Balin, and then enraged as he fights off the orcs occupying the dwarven halls. And Gimli maintains his pride even when death is near at hand when he refuses to be tossed in The Two Towers.
While Gimli and Legolas don't exactly hit it off, their relationship seems to change for the better with Gimli's reception of Galadriel. He is awed by her beauty and even asks her for her hair as his gift of choice. Aww, it sounds like Gimli has a little crush.
All in all he's a stereotypical dwarf; simple, direct, and stubborn as hard rock.