A pilot on an IPJ Runway 23 GPS approach reported taking evasive action and having a near miss after the aircraft's TAWS alerted about traffic. ATC was alerted after the fact.

Narrative

I was on GPS Runway 23 approach into IPJ and on frequency with CLT Approach Control. I was cleared for 3;400 FT direct IAF JOPAT; and then cleared for the approach. I was not cleared for switching to advisory frequency at this time. I hit the initial fix and started my descent per the published approach plate. Then I hit the intermediate fix and started the turn inbound onto the intermediate section of the approach and turned on my landing and position lights (strobes were on for the entire flight). About two NM before hitting 'CISBU'; I was still on with CLT Approach when my G1000 'TAWS' showed a target at my altitude and crossing my course a few miles out. I continued my descent and continued looking out the window to see the traffic. I picked up the high-wing traffic at my eleven o'clock and heading from my left to my right on a course that would intersect mine. The traffic did not have any lights on that I could see. I took evasive action that I felt would put me out of harms way - descending and to the right. At that point I managed a quick transmission to CLT approach that I was breaking off the approach to avoid traffic. After the initial turn I judged that the other traffic did not see me still and appeared to still be heading at me and that my current actions would not suffice. So I turned the opposite direction; to the left; continuing my descent to get under the other traffic. At that point; the other traffic appeared to see me and react by turning to their left and climbing. The other traffic passed in front of me and over top. Sometime very near that point; a different CLT Approach Controller warned me of traffic at my eleven o'clock and my TAWS system gave me an aural warning. CLT Approach then repeated the warning to me asking me to acknowledge but frankly I was too busy seeing and avoiding. After I was clear of the other traffic I then acknowledged. And after that; the original Controller took over from there and handled by IFR cancellation; etc. I do not believe that CLT Approach as any culpability here; and I believe that the other traffic's transponder wasn't being picked up by CLT. I actually think CLT Approach responded rather quickly to the situation; but still not as quickly as I responded because my TAWS picked up the traffic earlier. I believe that if the other aircraft had TAWS then we may have seen each other earlier and reacted more appropriately and safely. I also believe if the other aircraft had strobe lights on I would also have seen it earlier.