Lots of different ways to handle the under stairs opening. I've used plastic lattice cut to fit, a piece of plywood that can slip between back of step and wedge between RV Body, I've used a piece of hardware fabric(think chicken wife but smaller openings and stiff)....this works fairly well because you can re shape/fold it depending on distance between ground and stairs! In a pinch you can use those plastic jack pads with a little ingenuity....lol.
One other quick note, some campgrounds limit the height of your doggie pen to 24" ....just for info.