I feel that goats cheese just wouldn't have the right texture for it. Too soft. Really, if you can find cheese curds, they are the way to go. They get a bit melty, but stay nice, springy, and squeaky. They make a wonderful counterpart to cripsy french fries.
I also usually use beef gravy, but I imagine chicken gravy could be just fine. I've had poutine with miso gravy before, and that was certainly delicious.