"Will I need to remove the rear axle to remove the trans?"
In your case, either unbolt the rear ... or unbolt and pull the engine forward/out. There doesn't seem to be much left in the way. Depends on what else you're planning on doing/detailing/replacing. Piece of cake working with a bare chassis.
" ... will these two long bolts connected to the rear of the block & frame be enough to hold up the engine with the trans removed or will I need to support the rear of the engine below?"
No. Put some sort of jack under rear of the engine (unless you decide to pull the engine.) It also helps to adjust/align the stuff when you reinstall.
From the looks of your chassis so far, you could either pull the engine & trans as a unit or disconnect the rear axle from the frame & support the engine. Generally, when the cab & bed are mounted, you would support the rear frame then disconnect the rear axle and pull it back far enough to clear. Next would be support the rear of the engine then pull the trans out. Most of the 30s & 40s cars/trucks had trans access cover plates that can be removed in order to lift the trans out from the top or lower it down to the floor (which ever is more convenient). The load can be lightened by removing the shifter top.
Kerby
Thanks,
I've decided to remove the axle and leave the engine in place. Will take pics of progress.