You'd most likely end up with better accuracy, and flatter trajectory if you'll just stick to a mid weight bullet like the 165g Nosler balistic tips, or pretty much any other mid weight spitzer style bullets.
Light bullets start out fast, but at extended ranges(300+ yards), the mid weight bullets usually end up having a flatter trajectory. When using something like the 30-06 on prarrie dog, or groundhogs, it's gonna smack'em hard no matter what bullet style you hit'em with.
With the recoil, and handloading component consumption of the 30-06, you'd really come out way better in the long run if you bought yourself a good 223. Even if you just bought a NEF Handi-Rifle($250 or less) you'd get a lot more fun out of it in my opinion.