Outback is one of the better operators in the Tampa job market, which is reltively small. Don't mean to sound harsh, but 1000 isn't even close to what it would normally take to work there. For a Westwind SIC, try more like 2500+ with some pretty substantial jet SIC time or turboprop PIC time.
Tampa has always had enough pilots willing to move there and be "paid in sunshine", so there is no shortage of pilots there. Even in the best of times, 1500-2000 hrs was pretty much the bottom for a decent SIC position in a jet that required 2 crew in the TPA area.
I would say that in this job market, 1000 hrs is, if you're really persistent and really lucky, maybe enough to get on with one of the bottom-feeder air ambulance companies or other 135 operators at TPA or PIE, but only if you have 100 hrs jet SIC from somewhere else . . . . most of the crappy operators don't even want to spend the 5-10 hrs it would take to get you up to speed for a minimal 135 SIC check. Then they pay you by the day, and only when you fly.
Good luck, been there, done that, moved on . . . .