Pathfinder 1E Building a Lumberjack, need feat & trait suggestions.

I'm building a Barbarian (Mad Dog Archtype)/Brawler (Wild Child Archtype) Lumberjack. He'll have a War Bull animal companion with the intent to take the Mammoth Rider PrC for a Huge-sized pet. The Bull's name is Babe. He'll carry a Great Axe for felling trees and a Lucerne Hammer for pounding posts into place.

Are there any feats or traits that would provide advantages to cutting down a tree? This guy will be clearing forests, building forts, log cabins and roads in his down time.

Any help would be appreciated, thanks.

For one a Lucerne hammer isn't what you think it is. It has a small hammer like head but it's a pole arm and the head will have protruding parts so it will bite into whatever it hits. Hitting something wooden with this would end up with it getting stuck. Also pole arm, not a very barbaric weapon. Maybe go with great club to simulate somethings like a two handed hammer.

Inspired by Paul Bunyan/John Henry?

For the hammer schtick, you want a maul or a throwing hammer.

I don't remember my Pathfinder feats well enough, but I'd look at things like Power Attack, Cleave, etc. 3.5Ed had Sunder, which would be appropriate.

Of course, you're going to want to have the ability to Enlarge yourself and/or Babe. So a couple of Sorcerer levels might be appropriate if you want to be able to do so independently.