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

I am over the water in Nelson. I also tried to program the horn to do the chirp. I got the control to turn it on and off on the MMI, but no noise.

I am collecting the parts together. The siren goes in the plenum chamber and has to be wired through into the car and connected to a pin on the onboard supply control unit. The motion sensor sits in the overhead light and needs at least one wire to join the common LIN bus wire from the siren. The last part seems to be the switch in the door, which has 4 wire connections to the door controller. This looks the easiest, having previously fitted puddle lights to a Golf.

Still waiting for one connector, then will see if I can find a few hours to start running cables.

I was able to configure the chirp directly from the MMI interface, and did not need to use VAG or any 3rd party tools.