Strong recommendation: don't leave yet!
As has been mentioned, nobody wants to hire a "career copilot." While some outfits (regionals, etc) will hire low-time guys, the places that can be more selective want to know that you you have "what it takes" to be in charge of a moderately large, complex, expensive airplane. And the litmus test for that is Turbine PIC time. If you have 1000 hours of turbine PIC, then that means several things:
1. Somebody entrusted you with their expensive, complex aircraft
2. They kept on trusting you with it for a significant length of time (i.e. you didn't screw up too badly in their eyes during your time in charge)
3. You have what it takes to fly such an aircraft & not get violated or otherwise in too much trouble
4. You can probably learn to fly another complex aircraft.
On the other hand, seeing somebody get to the point of being about ready to upgrade, and then leaving, raises a big, nasty question: WHY NOT? And the lingering suspicion is, "because somebody thought he couldn't hack it." And that is a stink you do NOT want to have to overcome when applying for a job. You can explain that you left the job for greener grass (better pay, better qol, be near fiancee/family, whatever), but that's what somebody who got told "you might as well go elsewhere, we aren't going to put you in the left seat" would probably say as well. All the explanations in the world don't erase the stigma. And when somebody is looking at narrowing 6 resumes down to 2 or 3, things like that are a VERY clear discriminator.
Upward progress reflects well on a pilot; leaving in lieu of progressing reflects very poorly. Your call about staying for 1000 hours TPIC (I'd strongly recommend it, and more if you can -- turbine PIC time is turbine PIC time), but even if you just stay for 400 or 500 hours before moving on, don't leave now. The "greener grass" explanation is far more credible when you've proven that you CAN hack turbine PIC for several months, than when someone is looking at your resume wondering why in the world you didn't stay & upgrade, and forming his own (not so favorable) conclusions.
Best of luck in your upgrade!