My father, before his passing took two Adirondak deer with standard Remington 240gr JHP from a S&W 29-2. He did ask me if there was a .44 Mag load that wouldn't go all the way through a deer....
I suggested he try some of the 180gr, but sadly, he never got to the woods again to find out.
With a carbine, I would expect it to be a bit easier to connect well at longer ranges than a handgun. Since the handgun clearly works, the carbine will also clearly work for the job, if you do your part.
You don't need 300gr monster loads for whitetail. Any 240/250gr will do the job just fine. I expect (but have no personal experience) that a 180gr would also.
The cartridge has plenty of power for the job in all common loadings. The biggest drawback to a carbine is that often their sights and triggers are less than the best possible. If that isn't the case with your carbine, you are well set to bring home the venison.
All else being equal (and it almost never is) bigger bullets tend to work better.