Not sure what I have? So far this is what I have found. Barrel does have a stamp. I think its a proof mark? Also noticed the alignment marks at barrel to reciever bottom are on both and aligned.
Reciever - Quality Hardware 187xxxx Barrel -UNDERWOOD 2-44 Flaming bomb, Stamp - looks like a P with a R below down near bayonet lug. barrel band - K1 Hand guard -RMC Safty -E.I. Mag reliese - M & WA Rear adjustible sight - J.A.O Cannot find anything on the stock.
Your QH would be in the beginning of the first block of QH assigned serial numbers. The carbine has been through a typical rebuild post war and that is when the barrel was changed and the rest of it was updated with all the latest parts.