A greataxe 5e is a military two-handed melee weapon at the axe weapon group. A greataxe includes high crits, dealing an excess 1d12 damage at levels 1-10, 2d12 damage at levels 11-20, or 3d12 harm at par 21-30, on a vital hit.
Being a Halfling has minimal bearing on constructing your Barbarian; more significant for construct is your Barbarian style you desire. That said, Stout Halflings make remarkably resilient Barbarians; +Dex and Con Con means better AC (armored or unarmoured) and better HP.
The Greataxe has got the “Heavy” feature, making little creatures have drawbacks with it. A Gnome is creature size small, so you’ve got drawback. Rage does not add an edge to attack rolls, so you would still have a weakness.