The quickest way would be to purchase another tree. That would easiest and cara cara navels are easy to find. Short of that, you can either try to root a cutting or graft a cutting onto another rootstock. I don't know much about grafting, but others here can help you.

Too easy to do a bud graft (T-bud) to a rootstock good for your area. The first time I tasted a Cara Cara orange, I didn't even know what it was; but at that moment, I knew I had to have it.

You should not have any problem finding Cara Cara oranges to plant in Louisiana, I think that both the major citrus nurseries in Louisiana sell them (Star Nursery, and Saxon Becnel, both in Belle Chase) Star Nursery calls them red Navels, I am not sure about Saxson Becnel (their web page has been broken for a couple of months). Paul Becnel Nursery also sells them as Cara Cara's and are (or at least were) the local citrus nursery shipper for lemoncitrustree.com with there perpetual sale ending today. Star nursery or Saxon Becnel supplies almost every retail nursery (including big box stores) with their citrus plants. If you can't find a local nursery with them you might want to email Dawn Camardelle at Star nursery, I have found her very helpful in the past.