Okay, couple things about peas. First, they aren't going to start sitting on the eggs until there's a full clutch, at which point the hen will start sitting (if she ever does). Until then, it will look as though she is ignoring them. Eventually she may start gathering them together. Since peahens typically only lay every other evening, it can take a week or two for her to start sitting, or even a bit longer.
Second, some hens take awhile (a couple of seasons) to get the hang of it, and some never do. Third, yes, she may be much happier without the male once she starts sitting. Fourth, peahens lay eggs on dirt/shavings/straw (whatever the bedding in the pen may be) scratched out into a shallow depression, so putting one on wire to lay would be unkind at best.
These are not chickens.
Peahens, when they get the hang of it, make wonderful mothers. You can encourage her to gather the eggs together and/or lay them together by putting a few ceramic "duds" (fake eggs) in whatever scrape she may have started for her first couple of eggs. That may also signal her to stop laying sooner. I used brown ceramic eggs (Tractor Supply and other sellers online have them) and it helped my hen a lot. At five, there's a good chance she will see the process through. When the hens are only two or three, it's a bit harder for them to figure it out. Keep track of when she starts sitting (she may have 5 or 7 eggs by then, or even a few more). It takes about 28 days to hatch peachicks -- try to keep things calm and quiet around her. When the chicks start hatching, the male definitely needs to be out of her space so she feels safe.
If a peahen feels unsafe, she may abandon her nest.