Well, the consensus seems to be two of us saying it's got a belt (and in my case I can confirm that categorically) - one of us says it's got a chain (and I provided you with some suggestions about why this might well be the case - as indeed you too seem to reference). My Haynes manual references a timing belt. Why not whip off the timing belt upper cover and take a look? There are, to my knowledge, A4's fitted with engines with a timing chain - the big V8 is if I'm not mistaken. It certainly has issues with the tensioners at higher milages.
To my certain knowledge the one I have has a belt. You've referenced a chain driven engine - what's the source of this? Is it the same as the link I provided you with? Which clearly implies there may well be different engines fitted in different markets. Asking for advice on a UK forum is likely to be a little biased to the UK market.
Two of us have suggested speaking to Audi and outlined why you should speak to Audi. So have you followed this advice and what does Audi NZ say?
As we've advised, they'd tell you what it has and what the recommendation is for changing it. As to replacement cost, I guess it's a little hard to advise you on that without knowing parts and labour costs in New Zealand. Which may be different from here in the UK. General advice is change the waterpump and thermostat at the same time, and probably the other aux belts while it's all apart.
The invoice I have from 2010 shows it cost £239.59 to replace the t/belt and Vbelt, and water pump. The garage notes a recommendation to change the belt every 60k miles. Audi told me that or 5 years, whichever came first as I recall. The exact amount of labour isn't noted, other than £60 + VAT. Which would, I suspect, equate to a couple of hours, way back in 2010.
Mike
