Hi Ganderite,
It could be. I've heard of a few other collectors who have claimed there original Canadian Contract 1911's were also missing the J.
There are some documented 1914 Commercial Colts that with original barrels missing the J. Clawson's book on the subject also says it could be correct for the serial range. I would be a little more comfortable if the J was also there, but it could be okay.
I have not bought one yet with only the P, all the ones I've seen also have the J but it's possible some Canadian Contract 1911's only had the P on the barrel hood. I'd love to get into the War Museum's vault and do some more research on the examples in there.
I think there's a good chance the barrel you found is the original if it otherwise matches the one I've shown above. Check also to make sure they J is not very lightly struck, I have seen them before where it's hardly visible.
I hope this information helps, this is sort of a complicated question!
-Steve