Calbear is correct, the P-80 could have been ready at least in limited numbers by 1944. Only thing was it simply didn't have the range that the piston engined aircraft did at the time, the Germans and Japanese didn't have any serious counterparts deployed at the time, and a couple of prototypes suffered mechanical failures that delayed the deployment.
If it had been deployed, it would have most likely been used for the European theater.
The biggest issue that deploying the P-80 in 1944 through the end of WW2 would not necessarily result in any noteable differences in how the war plays out.
The big difference would be what potential changes might be introduced to later variants of the P-80 and future jet aircraft, which may or may not have an effect on aircraft tactics in Korea. At the very least, some ground combat tactics against real targets might help to develop some more effective tactics sooner.