Where to begin with this one…
Engineer is a combination defense/support class, with a major emphasis on defense. The most offense they get is when they wield the gunslinger, and even then, they are still reliant on Combat Minisentries to fight due to their squishy hitpoints. A good engineer always relies on his buildings, no matter what role he's trying to fulfill — an engineer that tries to do it solo can even be bested by a medic of equal skill, even WITH the Gunslinger. The moment an Engineer fails to have the cover or aid of a sentry gun, he's in extreme danger to even the weakest of classes if they can play them right.
Applejack, meanwhile, is a headstrong, run-into-trouble type character, by my understanding. She's a rodeo pony, and seems to be physical if she's forced into any form of conflict. Far as I can tell, math isn't her game, and the most advanced technology she utilizes is an apple cart. The only building we see her take any part of is in raising a barn — and even that's spent mostly singing while everyone else does the work.
With the Engi's squishy hit points and aversion to direct confrontation, we immediately have a problem with this match-up. Applejack doesn't seem to me the type to rely on a machine to do her work for her. Maybe it's just me, though?
Don't get me started on teleporters.