Got this info from a member at gardenweb. I underlined part of Christine's response to another member living in Houston. So, apparently, if you get the seeds to sprout, keep the seedlings in containers during the winter, plant them inground in March, get fruits in November.
The link to the entire thread is:
Red Lady papaya photos - Florida Gardening Forum - GardenWeb
Randy---It sounds like you are determined to grow papayas. So, I will do my best to tell you how.
For next year:
Your papaya seeds need to be started in the summer and potted up until your freezes are over. The size of young plants would not be so large that you couldn't lift them. For the plant you have now I would use a "hand truck" to save your back. I am a petite built woman and this is what I use for heavy plants.
If you are able to plant the papaya plants in the ground by mid-March, you will be eating papaya starting in November. Keep in mind that they are heavy feeders and like a lot of compost. The compost also helps the plants to not dry out. Papayas thrive in the tropics so your summer heat will not be a problem.
Papayas get a sizable root system so if you put them in a pot that is too small it will stunt the plant. The dropping leaves can be caused by letting the plant get too dry, too cold, or not enough sun from keeping it inside too long. Keep the plant that you have now in a large pot by itself.
As for variety, the plant you have now came from a grocery store fruit which may not grow true to seed. I tried that once and the fruit tasted terrible. It is best to get a named variety such as the Red Lady papaya that I described in an earlier post. Another advantage to the Red Lady is that it is a dwarf and all of the plants are self fertile. That means no male is required so you could grow just one plant if you wanted.
A friend gave me 2 papaya plants recently that are extra dwarf and grow easily in pots. If I get it to fruit and produce seeds next summer, I will post that I have seeds available to give away.
Hope that info helps. Good luck.
Christine