Hogging out means marking the circle, then using a jig saw to cut just a little outside the line you drew. Not more than 1/4 inch. Then you make passes with the bit, with a 1hp router, you will have to make many passes, and I'd limit it to 1/8th inch of depth per pass. That means you'll be extending the bit 5 times to cut through 3/4 inch of material.
You need to have the center of the jig securely affixed to the table's center. The easiest way to do this is to drill the center hole on the back side of the table so the hole isn't visible when the table is finished. Just driving a nail will allow for a little slop that will not only spoil the circumference, but interfere with having the bit track exactly through multile depths
Alternatively, use a small piece of ply and double-sided-tape it to the underside of the table top. Pre drill a hole for the peg in the small piece. If you're fussy, you can take another same size piece and double stick tape it near the end of the circle cutting jig so the bit is going straight down into the top rather than at a slight angle. The closer you rough cut to your marked line, the more you can remove with the router, but again, 1hp is a pretty low power tool.
Hope all that makes sense.
BTW, the biggest hassle you may have is the power cord getting in the way. I tend to hang the cord from a swivel clip (amazon has them) above the workbench so it stays out of the way and doesn't tangle.
The more I do, the less I accomplish.