Will it hurt my baby fig tree if I transplant it into a big pot now? It just started leafing out.?

Depends on where you are located and whether or not the tree is kept outdoors or has been inside for starters. Since it is just leafing out I would not transplant it or you will risk loosing it to transplant shock. Usually a fig like this can be potted up either when its dormant or in late spring if needed. My preferred time is usually when they are dormant as its less stressful on the tree. Also since it is only about a foot tall I do not recommend up potting it at this time. Wait until it is at least 2 to 3 feet tall to do this. Figs actually do fine when they are root bound. And when potting up a good general rule of thumb is to go up by one inch in pot size since it is in that outer inch that most root growth will take place actually. See if you can find a 2 gallon standard or a 2 gallon squat type pot, (These are wider and flatter than the standard ones.), when you decide to re pot the fig and take it from there. Good luck.