Take the Mini away from the van.
Clip it on the back, walk to the ridge, the beach, the top paddock. No cable run to the vehicle, no generator, no 240V. Just the dish and a battery shaped to fit it.
Be honest with yourself first — do you actually need this?
If your Mini lives on the roof of the van and you're parked up, you don't want this. You want a booster at $65, running off the caravan battery you already own. It'll run the dish all week, not five hours.
This is for when you're away from the vehicle. Dish on a tripod chasing a clear patch of sky. Fly-in fly-out. Backup when the van battery's flat. That's the job.
And it doesn't need a booster. Most batteries put out 12V, and the Mini won't hold a steady connection on 12V — which is why people end up buying a step-up converter as well. This one outputs 15–21V DC direct. Straight into the dish. Nothing in between.