The best time is during active growth so the roots have a chance to heal, so unless there is urgency, next spring would seem to be ideal

Do you have suggestions for planting around a pool in zone 8?

Just a word of warning your bird may stop flowering if it is put into a pot that is much larger - they like to be pot bound to flower - I would remove the pup and put it right back into the same pot again.

Cheers

Jeff

I know it's really late posting (been in hospital for quite awhile), this is the city flower of L.A., and Jeff/nyssaman is correct. A pot maybe 1-2" larger. They bloom best root bound and untrimmed (thinned leaves) unless the leaf is dead, of course. In the ground they are "neglectors" not much water or food, no thinning out, etc. I can't be zone specific, but they love it near pools. From my experience, they can be virtually ripped from the ground and stuck in a hole and thrive. (Don't try this at home :) All good things to you, my friend!
-Don

Waterlover: Bananas. Not the most original idea, but they do well near pools.