This will be a species of Ficus.

I never would have guessed a ficus. It's young (under a year) and I am going to transplant to my yard. What season is best to do this?

Southern magnolia?

Ficus for sure.

The only ficus I found that looks like this is the rubber tree..could I be right?

F. elastica tends to look different. That leaves more than 800 other species to choose from.

...and in Florida, nearly all of those 800 will thrive!

Should I keep it in a pot outdoors or indoors or plant in yard? Wish I knew for sure what it is :(

How did you get it? Did it come up in the yard? That would indicate a parent tree growing outside there, doing well enough to be producing figs.