Has anyone any experience of retrofitting the Audi alarm to a Q3. I have a 2014 which is a Japanese import into NZ, and it has convenience key and immobiliser but no alarm.

Looks like you need the siren, motion detector and door switch, but from an inspection there is no cabling to connect the units into the car systems.

Wondered if any one had done this; suspect to do the cables run and find the right connectors it is not worth while.

I haven't.
I am also in NZ (Wellington) and have a NZ new Q3, which only has immobiliser as well.

I was interested in installing an Alarm, as I wanted the Alarm "chirp" when locking/unlocking the doors. I have tried programming the Horn to do the chirp, but doesn't appear to work (but didn't spend too much time on it so far).

I would be keen to hear how you go with the OEM alarm.

I have a Q3 in America and mine makes the chirp noise when you loch the doors using the remote. I have a 2018 Q3 and it works and even it worked on my 2015 Q3 too