If the monitor`s 30cm (12inches) total length, it`s possibly sexually mature. I`m not sure what ga is? I`m Australian, but living in England at the moment!
I`ll make a guess Georgia, and then ask is it similar to the African savannah where these monitors originate from (tropical)?
If the temps and humidity are suitable then yes, it might benefit the animal to spend some time outdoors, obviously, you`d need to make sure there were cooler/shadier places to retreat to, and check the temps very carefully..