You are looking for a wet bag?
Wet bags are simply waterproof bags to transport wet or messy nappies.
– Wet bags may be large, small, have a zip, a pull cord, velcro or hang on a doorknob. They may be PUL lined, or made out of fleece or wool. – Some wetbags have a matching pair – one for dry, one for wet things. – You’ll need to have wipes, so consider a nappy wallet or nappy bag as well. – They have the eco benefit of being reuseable.
Now you can browse retailers offering wet bags in Australia or in New Zealand:
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