It hasn't rained out at Palm Valley for several weeks, so you should have little to no water crossing to do. WH should be fine.
Palm valley has two stages to it. the first is the entry from Hermannsburg to the campground, the second from the campground into the valley itself. the first stage is easy enough with tyres aired down a bit (more for comfort as it is rocky), the second stage can be slower going, but if you have more clearance than a Subaru Outback, you shouldn't get stuck at any obstacle.
The terrain changes constantly, and it's rained since I was last out there, and the track could have changed course a bit. the main parts stay the same though.
a tank of fuel should easily get you out and back from Alice to Palm Valley. there's a sharp dip in the road a few minutes out of Hermannsburg that is sure to excite at 110kph, might pay to wash some speed off, you'll know it when you see it.
Attached is the 4wd map and information from NT Parks and Wildlife. Best advice is if you don't think you can get past the camp ground in your Jeep, it's easy enough to walk in to the tourist walk section.
http://www.parksandwildlife.nt.gov.a...-4WD-Route.pdf
NOTE: there are two paths to walk at Palm Valley, a high track and a low track that follows the river. if you can cope with the step climb, the high road is worth it for the view at the end. The low road is great too, but scenery from an elevation is always more spectacular