Hi and welcome! My fig tree drops leaves when it gets that rusty fungus - the reddish spots on the leaves. It doesn't kill the tree and it puts on a whole new set of leaves after that happens, then it loses all those leaves for the winter as well.
No worries, I wouldn't think. Don't take off any of those base branches until the tree is a lot bigger. After you plant it out at your new home, let it grow all it wants for a couple of years, then you can limb it up (cut off lower branches) to encourage more of a tree shape. Early on, it just needs all the leaves it can make so pruning will only set it back.
