Everything I've ever read advises against making large scale life changes such as a major move within a year of retirement. Retirement alone is a major life change, with many moving parts (i.e, financial, psychological, emotional, identity, activity, etc.). It's disorienting for most, and downright disruptive for others. Adding another major change such as a move (let alone moving to another states) complicates things and dramatically adds to stress.
If you've done your research (and I'm assuming you have), you must already be aware of how different Georgia is from California (lifestyle, climate, culture, etc.). I would personally never make such a dramatic change immediately upon retiring. If it turns out you later feel you made a mistake, it will cost you financially to relocate yet again.