Harriett,
If you can be patient the best time to move plants is in the Fall and this is fast approaching. I would further suggest that you go ahead now and prepare the spot where you will move this plant to. Dig a spot not necessarily deep but wide and amend the soil and of course remove the weeds. It needs to be a sunny spot for pomegranate. I'll bet the variety you have is 'Wonderful' as that is what the nurserys sell just like they sell 'Bartlett' pears to an unsuspecting public. There are better varieties out there but it is okay.
It may take your plant several years to become mature enough to begin flowering and fruiting but it is well worth the wait. I suspect most people don't know the hardiness range of pomegranates. I know they will grow north of Mexietta (formerly Marietta).

It's actually "eversweet" which was offered by peaceful valley garden supply. It sounded ideal for GA climate. tolerates heat and cold, and very likely to grow back from roots if frozen to the ground. It was marketed as much better than "wonderful".

I suspected fall was the best time, my compulsion to move it has passed. I moved some candytuft and killed that instead. A much cheaper sacrifice.

thanks, Harriet