Volkodav,
Don't have much to expand on your question, but its interesting you brought it up.
The other day I "rediscovered" a book that I've had for over 30 years, "Warships of Australia", by Ross Gillett.
It briefly metions, as you said, the County's were also considered, so I also googled up the following on the Perth DDG's:
Perth class destroyer - Wikipedia, the free encyclopedia
You may have alread read it, it goes into a bit more detail about the decision between the County and Adams Classes.
The first two were ordered in January 1962.
It also mentions that at one stage consideration was to install "Tartar" on the Battle and Daring class destroyers, this did not proceed.
Then the third, Brisbane, was ordered in January 1963, also mentioned is a possible 4th, but no detail.
There was also one more interesting thing in the book that I'd forgotten, that was a brief mention of the DDL project, which started around the time of the Indonesian confrontation, so I googled that too.
Australian light destroyer project - Wikipedia, the free encyclopedia
Again you may have already read it, The DDL's were originally planned to be 10 ships, built in Australia, starting out as 1,000 ton design and then growing to 4,200 tons (the book is not in metric!).
The artists impression of the DDL in the book looked very much like a British Type 42!
The DDL project started in 1966 and was cancelled in 1973, and out of that grew the order for the FFG's!