The .30-06 is serious overkill for deer. Will it work?...Yes Is it big enough?.....yes Is it necessary?....absolutely not!

IMO the best calibers for deer (and deer alone) are the 25, 26, and 27 calibers.

The .243 you currently have is as good for deer as the .30-06 you're thinking of.

The .30-06 can handle any animal on the planet with the proper bullets and proper placement and that's been proven.

To me the best deer cartridge is the .260 Remington......take it from there.