It is lovely to think that you have trained your dog so well, and it seems that she is a willing participant. Sounds like a great relationship.
Love your photos of the fantail as well. We saw one at the Grampians thanks to beady eyed Bird watching girlfriend.
Yours is the Grey Fantail - other names: Cranky Fan, Mad Fan(?), Snapper, White-fronted or White-shafted Fantail. Personally I think Zachary is a most appropriate name for your bird.
Pizzey's Field guide to Aust Birds describes the voice as: An oft-repeated, fairly sharp 'dek'. When breeding, this develops into tinny but sweet, animated song of fiddle-like see-saw character, usually ascending, often ending in several drawn-out rising notes of silvery quality; surprisingly loud, prominent in dawn chorus.
On that basis I'm thinking your bird must be breeding, or at least trying to attract a mate. Lucky you. Look out for 'Zoe'.
Apparently these plucky little birds migrate across Bass Straight! That's phenomental for such a tiny bird.
