I have never successfully grown key lime, but my lemon trees bloom in early spring and the fruit ripens by the first of the year - so 9 months, perhaps. It keeps well on the tree, so we can pick it for several more months. The tree will start to bloom again before we have picked all the previous crop.
Your little trees could probably profit from feeding. Be sure to follow the directions on the citrus food; potted plants normally require diluted fertilizers.