I have been eating veggie dumplings recently so I am asking for suggestions for what sauce to serve with them (especially with sesame oil). I am in New Zealand.
Traditional dumpling sauces should be vegetarian already. For example, Japanese gyoza are served with shoyu (soy sauce), komezu (rice vinegar), goma abura (sesame oil), and chilli oil (optional). I see no reason why you couldn't use these with veggie dumplings.
Check that products from South East Asia do not contain fish sauce but this should not be an issue for Chinese, Taiwanese, or Japanese dumpling sauces. These should be available in international supermarkets in NZ and if you want to be sure then you can make it yourself easily using the above ingredients. Here in Japan, we often make the sauce ourselves rather than buying it pre-made. Most Chinese and Ramen restaurants serve them separately to mix them how you like. I'm a New Zealander living in Japan so I'm confident you can get all the ingredients needed in most NZ cities.
We also often use "ponzu" or "miso" paste for sauces in Japan but these may be more difficult to find in NZ. If you're strictly vegan, bear in mind that soy sauce and miso products may be fermented using lactic acid bacteria which may be sourced from animal products, although some vegan alternatives do exist.