One year should not cause any issues. I had a 69 GTX that sat for 20+ years with a Carter AVS and I took it apart cleaned it up and the only piece that I replaced was the accellerator pump. As far as the engine, I pulled the rockers, freed up the valves, pulled the plugs and poured some ATF through the engine as it turned, put new plugs in and it ran really well.
As far as What carb you have I still have to say a Carter AFB, because if you had an old 4160 Holley you would have said.. "What carb is this, it's leaking gas everywhere".
If you have never messed with carbs before I would suggest that you find someone that has a reputation for being honest and doing mechanical work with positive results to do it for you. As far as what carburetor, you will be able to read Carter/Holley etc, right on the thing somewhere. If you want to buy the kit you will need to get numbers from the carb itself or an aluminum tag on the carb.