Yeah. "Hunters" will randomly take a "hunt" job where they will go after an animal on the map. But they will not hunt if they don't have crossbow, quiver, and ammo. They won't hunt with other weapons. They act glitchy if you have them in a militia squad with the hunting labor enabled.
Note that you can make crossbow bolts and crossbows out of bone at a craftdwarf's workshop and a bowyer's workshop, and a quiver out of leather at a leatherworks. Leather comes from tanning the skin of butchered animals, which is also how you get stacks of bone.
If you want them to kill animals in melee, first you need to have the weapon created, have a military squad created with them in it, and them set to use the weapon--anything from "Use melee weapon" to setting them to use the particular weapon you created for them. You also need to MAKE SURE they have Wood-cutting, Mining, and Hunting labors all turned off, or else bad things happen. You then have to go into the 's'quads menu, issue a 'k'ill order, then go find an animal and order it to die. Be warned, however... Military dwarves will bum rush animals, who will almost always flee. Unless you have another squad, WITHOUT kill orders, set to m'o've behind them to cut them off and kite them into an area they can't escape from, you likely will never catch them.
You also have to take care with the corpse. You need a butcher's workshop, you need a stockpile set to accept corpses, they need to be VERY close, and the dwarves need to take it there. You might have to unforbid the body, and you will definitely have to go to the 'o'rders menu, 'r'efuse, and tell them to gather refuse from outside. They must haul the corpse to the stockpile, and they must do it in time before it starts rotting. You must then queue up a "butcher dead animal" job, and then pray. I have never successfully butchered a corpse.