I’m from the UK, now living in Wellington, own a 250cc trail bike. You would be most welcome to stay with me if you’re passing by 🙂
You’ll find buying a bike is more expensive here in NZ, mostly because there is less choice.
If seat height isn’t a big problem, consider a DR650 or KLR650 – popular dual sport bikes and cheaper than a BMW. I’d also recommend bringing a set of soft throw-over panniers with you, again, lots of choice on eBay which doesn’t exist in NZ.
Depending on where you go, most roads will be sealed with only back roads being gravel. The BMW, DR or KLR would handle them well & your confidence will grow as you travel.