The only thing a rifle does differently than a pistol is push projectiles faster by using a longer barrel to full efficacy. So, what you'd be missing out on is more noise, more recoil, pricier ammo, and damaged backstops with the accompanying angry range officers. If you don't want a 22, then a pistol-caliber carbine is a GREAT idea. My personal dream would be a bolt-action in 9mm Luger, but those aren't available. You can make a single-shot 9mm rifle with a Thompson Center Encore and a custom barrel, but that can be expensive. There are many semiautomatic rifles in 9mm, 40, and 45, like the Hi Point carbine and the CX4 Storm by Beretta, and then there are lever action rifle by Marlin or Uberti that shoot 357 or 44 magnum. Depending on what you already load, any of those would be satisfying alternatives to a rifle-cartridge, and certainly no less effective for uses other than target work. Most deer shot with a 30-06 are taken at ranges within which a 357 levergun would have done just as well. A 9mm carbine with even a 10 round magazine would be exceptional at both 2 and 4 legged varmint control.
"... I cannot but conclude the bulk of your [politicians] to be the most pernicious race of little odious vermin that nature ever suffered to crawl upon the surface of the earth." ~ Jonathon Swift