Bought a Vintage Bianchi 1985 road racer, came with Shimano 600, can I easily turn it into index shifting? As my title says bought a:

Bianchi 1985 vintage in almost mint condition
Shimano 600, 12 speed (2x6) with freewheel, friction shifters
I'd like to turn it into an index shifter.

Do I just swap out to index shifters Shimano 6 speed?
And then get a Shimano SIS rear derailleur, and I'm golden? Are there different sizes I should know about?

Any suggestions? Anything else I should know?
I'll be happy if that's "simple". I'll try to tune it up as much as possible if not bring it to a bike shop. I'm very new to modding things and starting to learn and try things myself.

Thanks in advance!
Some pictures of the levers and the RD may be welcome and clarify the situation.

Shimano 600 was an indexed shifting system and stands at the beginning of the Ultegra line of products. It can be switched from friction to index by turning the toggle at the side of the right down-tube lever (if you have the original Shimano 600 levers). However if you have standard friction levers you'll have to find a pair of original 2x6 levers. Although the 2x6 thing bothers me a bit as the 1980s Shimano 600 tri-color that I own is 2x8 and cassette type instead of freewheel. It suggests that there are some non-original bits in your recent acquisition. Pictures please! 

Indexing happens in the command levers, there is no such thing as an indexed rear derailleur. So there is no need for acquiring a different RD if it is indeed a 600.