Mostly you'll be getting Theonite from daily missions and Prize Fights. It should take you between a week or two to get to 1,000, since you get about 55 per day from missions, and you get 55 for completing the progression of most Prize Fights. There's at least 6 character ones that offer Theonite per week, which works out to something like 47 Theonite per day if you're willing to make progression in all 3 of the bronze/silver/gold ones.
Then (55+47) x 10 days = 1020 Theonite
It may be a little faster or slower depending on the missions you get and how much you want to play. Also, I think there's another weekly Prize Fight I'm forgetting that offers Theonite, which would bring it down to 9 days to get to 1,000.