Well, our dog is much smaller than yours, but, in our expereinces off-roading, it depends on the situation.
For most of the ride, we have her harnessed, on a cargo rack (so she can see out), on a bed, and with cargo nets. Additionally, we added a small 12v fan for the warmer days. For the more technical stuff, she'll sit in my wife's lap, still harnessed in.
We found she does much better if she can see out. We first tried it with her harnessed in the rear seat, but being so small, she couldn't see out and didn't enjoy it too much.
Get your puppy used to being in the Jeep as soon as you can. Helps out later in life.