I'm no expert, but I've had experience with death wobble (it happened all the time with my '06).
I don't know what shop you are going to--independent or a Jeep place, but if they want to simply replace the steering damper then expect it to be a temporary fix.
It could be a stabilizer bar, bad front u-joints, ball joints, etc. Death wobble is very hard to diagnose.
I finally got rid of my '06 because of it. I don't blame the Jeep itself. I blame the crappy roads here in Syracuse. The Jeep never went off road, but I was replacing front end components on a regular basis. And death wobble always kept appearing. Almost wrecked a few times because of it.
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