Depending on whether you're trying to retain the "stock" look, you have a couple of options.... You can probably get replacement pegs on-line, but if you are like me you'd prefer geared tuners.
I'd replace all the pegs with geared tuners. The last time I bought an old uke with pegs I just went and got a $20 Hilo at my local guitar shop and scavanged the geared tuners from it. Some guitar shops may even be able to sell you tuners ala carte if they also do repairs. I had to carefully drill out the peg holes a little to make them fit right (although they may just fit). This may be a little more difficult on the metal head stock of a dixie. It can certainly be done with a steady hand (drill press would be best) and a good set of carbide bits... I might even consider taking it over to the local machine shop and having them do it for me.
Also you can just buy geared tuners on line, but again, if you're like me, you don't want to wait for that and the other parts from the cheapie may come in handy some time.
Good luck! Let me know how you decide to tackle it.
UB