Peafowl instinctively take dust baths to help prevent skin parasites. They will scratch a depression to roll around in, and that little dustbowl will be around 6" deep. If your hens nest on the ground, their nests will be about 4" deep. That's a lot of dirt, so it would probably be more cost effective to either bury the wire, or attach another length of wire and run it 2 feet our from the pen.
Another thing about buried wire - it will rust faster. With a good welded wire and medium rainfall, you might be looking at 6-8 years before it rusts out and the welds pop. Above-ground wire will last much longer than that. And it's easier to replace if you need to. You might also take a chance of your birds cutting their feet on rusty wire.
My peafowl are on grass and they love it. It harbors insects that they eat, and I let parts of the aviaries grow tall to keep the ground cooler during the summer. Yes, I do have to mow the grass in their aviaries, so I bought a manual rotary mower for that job. Depending on the size of your enclosure and the number of birds in it, you might not need to cut the grass because they do eat grass. Peafowl don't scratch and dig all over the place like chickens do - they choose one or two spots and dig their little bowls. You will probably only need to clean poop from under their perches. About 3 times per year, I take a shovel out and remove what's under the perches. Whatever is in the rest of the pen serves as fertilizer, and the grass grows quickly.
You are going to LOVE your peafowl.
