Luckily, these old Jeeps were built well! With heavier steel than you will find today.
The best bet, as mentioned earlier, is to do a lot of small spot welds, preferably with a MIG welder.
Fluxcore welders work also, but are not as clean, and require wire brushing to see what you just did

You can make a bunch of small tack or spot welds, like this:

The reason for this, is to keep the heat down, and therefore not warp the sheet metal.
Once you have the patch in place, keep doing small welds, until the entire patch is welded in.
Then, grind almost smooth, and finish off with a flapper wheel.
If you find any holes, or missed spots, it's easy to do some more spot welds, and grind/flapper wheel them down.
I have seen some repairs done that you would never know, unless you saw the before and after pics.
(I'm not that good, but it is doable!)
For small bolt holes, brazing works well also, but takes some practice, as the heat required is more than a MIG welder produces.