Headers and a different carb would probably make very little difference. As Max stated, the biggest problem is likely the heads, and possibly the cam. Fortunately, a lot of SBC heads will fit and can make a difference. More detail would be needed to verify what you have first.
The typical '69 307 had a 2 barrel Rochester, probably a 2GC, and large chamber heads with smallish valves and coincidentally small port runners.
Upgraded stock heads or aftermarket heads such as '416 castings from a later 305, or World S/R or Edelbrock E-Tec heads can provide better flow, and if you get smaller chambers like 58cc the static CR can be bumped to close to 9½:1 without touching the pistons. After that, a better cam will help the flow. That's the point where header sill actually make a difference, and a different carb would be in order IF the original is a 2GC. If the original carb is a QuadraJet, I'd stick with that and set it up for the new heads/cam.