Pilot flying C182 aircraft reported NMAC with a King Air on climb out at a non-towered airport.

Narrative

I was holding short at ZZZ during class E non-towered operations. A king air was on final and had just reported over ZZZ1 to the south. A Varga aircraft had just landed. I ensured he was clear of the Runway by asking. King Air air reported turning final; I entered the Runway and began my takeoff roll. King Air reported short final; and announced he was going around. When I took the Runway he was on a 3nm final. In his go-around decision; he did not initiate much of a climb. About the departure end of the Runway; he came over top of me at about 300 feet. I was climbing through 5800 feet MSL. It was his PIC decision to make the go-around; but by not performing a proper go around and climbing to TPA he created a larger safety issue. I induced his go-around decision; but 3nm mile separation from a takeoff and landing aircraft is sufficient in my opinion. Looking at flightradar24; the kingair was on final at 155 kts. which far exceeded his vref speed. I feel my decision to takeoff when I did was the right decision; but holding short and allowing the kingair to land may have been the better decision. His decision to go-around could have been more detrimental to safety.