Why even bother bringing it? If you are going to bring a backup firearm in the form of a pistol it should be at the minimum a 357 Magnum revolver. Only Magnum revolver rounds have the sectional density and velocity needed to dispatch large animals.
This is absurd, you don't need a magnum to give the coup de grâce. The best reason to carry a sidearm is to avoid the ugly mess you can get with a high powered rifle at close range. Any .32 or .380 would normally do the job without excessive hearing damage and the need to push the eyeballs back in.
I don't think the OP would be hauling an M1 if he planned to use the .45. I also doubt that the .45 was planned to be the primary gun in case the M1 falls apart; my understanding is that M1 Garands always work. Yes, he shouldn't have been so confident to sling the rifle, but this was an unplanned situation. It sounds like the choice was to sling some lead at close range, or hope to snap-shoot it in the butt with the rifle before it's gone from sight.