Just for reference:
Indiana will recognize your handgun license which will allow you to hunt in Indiana with a handgun. However .45 ACP isn't allowed for deer. You would have to check for the state your wanting to hunt in to see if they will recognize your handgun license and what caliber restrictions they have.
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IC 35-47-2-21
Recognition of retail dealers' licenses and licenses to carry handguns issued by other states
Sec. 21. (a) Retail dealers' licenses issued by other states or foreign countries will not be recognized in Indiana except for sales at wholesale.
(b) Licenses to carry handguns, issued by other states or foreign countries, will be recognized according to the terms thereof but only while the holders are not residents of Indiana.
As added by P.L.311-1983, SEC.32.
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Legal Handguns for Deer Hunting
Handguns, other than muzzleloading, must have a barrel at least four inches long and must fire a bullet of .243-inch diameter or larger. The handgun cartridge case, without the bullet, must be at least 1.16 inches long. Full metal-jacketed bullets are not permitted. A handgun may not be concealed. Handguns are not permitted on any military areas. Some types of handgun cartridges legal for deer hunting include 357 Magnum, 41 Magnum, 44 Magnum, 44 Special, 45 Colt, 45 Long Colt, 45 Winchester Magnum, 35 Remington and 357 Herrett.
Some illegal handgun cartridges for deer hunting are 38 Special, 38 Smith and Wesson, 38 Colt New Police, 38/200, 38 Long Colt, 38 Super, 38 ACP, 38 Colt Auto, 45 ACP, 45 Automatic and 45 Auto Rim. All 25/20, 32/20 and 30 carbine ammunition is prohibited also.
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Don't know firsthand what is involved for you to transport the firearm back and forth across the border.