Yes, rather obviously later than 1745: first printed in SMM after Burns' death in 1796 (see reference above). Like most Jacobite songs, written at least half a century after the event, in a sort of romantic afterglow. Please do take the trouble to read the other thread I mentioned, which should make it perfectly clear that Lesley quoted the wrong information when this old thread was young. The other thread also makes it clear that Burns, relying on Dr Blacklock, believed that the original song was about the Glencoe massacre (though there seems to be no direct evidence of that).

It's all there if you bother to look.