Leveling an alt with pet battles would be great to get the garrison monument, too, but is that character specific or account wide?
I mainly got lumber mill on my alt because I wanted to unlock level 3 plans faster for my main. Then I swapped both my main's and my alt's mills for a barn and I'm now trying to get enough work orders to unlock that one. Trading post gets stronger now that mats for work orders will get cheaper and cheaper. But definitely in the beginning it might have been expensive to keep work orders going. I had to buy furs for my tailor alt from the AH for the first couple of weeks, it wasn't too expensive though. I actually had to buy ore too before my mines started to support my JC/BS/engineering profession again, because you can level jewelcrafting with just ore and herbs.
I think if you want to level your alts via pet battling or whatever just somewhere in the future, get them to their garrisons asap just to afk there. That should help with not getting resources from questing. I've got plenty of alts but I've been lazy so I only have 2 other alts now sitting in their lvl 1 garrisons, gathering resources. Sometimes I do some missions with the 1-3 followers they have. They have ~3600 GR now just from sitting there. I can thank the bugginess of the launch for getting 4 characters through the dark portal on day 1
I also noticed that I don't really need to upgrade my alt buildings to level 3 just yet. I have no energy to properly play with alts right now, so I don't really care about how fast I level/gear up followers, my alt or anything. Still it would be great to get another lvl 100 alt for another pet menagerie in the near future...