Hi Catahoula,
Sorry to be slow responding. We're in the process of training up a service dog for my daughter and whew! it makes training goats for carting seem like a walk in the park!
I love your goal of carting/dragging brush! Your goats will too; some have a great work ethic (and others are just here on earth to bless us with their beauty and much browse, or at least one of ours is under that impression).
There are other folks on the forum with so much more carting experience than us, so I hope they chime in. We got our Saanen boys for carting rather than packing, though we are far (far!) from experts. I'll just tell you what has worked for us, for what that's worth.
We started with leash training and collars. Our first pair of boys were probably the age of your goats when we started; we started our second pair at mere weeks of age. Corn Chex can really help with the skittish tendencies.

Get them used to walking calmly beside you on a leash; it's an important skill overall. Not that this EVER has happened to us, no....but sometimes naughty goats escape when absentminded moms (not that moms like myself are ever absentminded) leave the gate open and neighbors find the goats pruning their roses and they have to be lead home again. That skill of calm walking on a leash comes in mighty handy. Ooops...MIGHT come in mighty handy in the event such a thing would ever happen. Not that it ever has before...
Once they were walking calmly on collars with leashes, we moved up to halters. It was a pretty easy transition and it made the boys easier to direct on leash. We worked on "walk on," "whoa," "back," "left" and "right" (because certain moms who would never be absentminded can't keep "gee" and "haw" straight), and "easy." We did lots of walking on leashes practicing these commands. I liked clicker training and a target stick to introduce left/right/back.
We didn't even put harnesses on our boys until they were a year. We allowed the biggest one to start pulling very light and extremely well-balanced weight at 200 lbs (about 16 months...he's a big boy!). He will push with his head if we don't let him pull, but he's still just 2.5 years so we are careful to keep his pulling very light and balanced. We want to make sure his skeleton is developed fully to pull weight.
We've got a Sacco cart that needs some wider shafts made (goats in excess of 200 lbs are quite a bit wider than a carting dog breed), at which point this fellow will be allowed to pull our 90-lbs daughter around the pasture. At the speed we move, he'll be 3.5 years before he has that chance.
I know of a gal whose goats learn carting by pulling a travois, which is also a tidy way of carrying downed limbs over to the burn pile. It sounds like a great idea to me. Still, you wouldn't want to add any weight until they were three years or so.
Enjoy your goatie buddies! Yes, they can be a lot more fun than decorative weeders.