Whatever she's dragging, have it connected to her collar, and have the chain long as Laura described. If she does jumpt the fence for some reason, she needs to be able to stand on the ground and pull the tire over the fence after her.
I've only ever worked with one guard dog who would jump a fence when he had a tire dragging. Old Luke was 120 pounds of numb-skulled and single-minded determination to get coyotes away from his sheep, and then to get back to his sheep.
On one occasion, we were moving his sheep from one end of the field to the other and didn't have enough hands to keep him from straying onto the adjoining road, so we looped his chain (2/0 zinc-coated) around a telephone pole that was a support for a pole barn.
You guessed it. Luke joined up with the sheep, having pulled a link out of the chain. When I first saw him coming up behind us I half expected him to have the pole barn behind him, clanking along, dropping sheathing and roof boards along the way.
Anyway, Luke had about eight feet of chain and a tractor front tire. He would jump over fully-charged electronet to get at coyotes, and then pull the chain over. He must have been getting the shock the whole time. Then when danger was past, he'd jump back in. The only problem was that he never jumped out and in at the same place, and he invariably flatted a section of net at each point of traverse.
Every other dog I've worked with has been respectful of electrified boundaries, although a couple of bitches I've had were capable of slipping through the bars of gates.
My young guys went from a car tire to a lawn mower tire to no tire at all -- just the chain -- and now to no impedimentia whatsoever in the course of about a year.
The key thing here is to not give up on her at this age and at this point in her introduction to your flock. It will take a few more months, but you'll be very glad you stuck it out. And the next one will be 1000 times easier, because the sheep will do part of the training for you.