Thank you for the above advice, some of which I understood.
The only problem would be acquiring the dog. It's not my dog. If it was, it wouldn't bark.
I do still have a plan. Not quite like the original, but I would still need the detector circuit, with an electret microphone. There are various levels of sensitivity, so I'd have to try a few out.
Any advice is always gratefully received.
I did read a story (unconfirmed but credible) from the USA, which, for once, wasn't "shoot it". The neighbours installed a traditional microphone, amplifier and hifi speakers pointing at the offending dog owner's house. Every time the dog barked, the sound was amplified to be four times as loud and sent right back where it came from. When the police arrived, they said that (see chain of causation) the dog owners were responsible and the neighbour was right within the law.
However, as fun as that might be, I prefer the discrete path.