A NSW greyhound with a muzzling exemption (a Greenhound) is only recognised within NSW. If travelling to another state you must contact the relevant body in that state to find out the requirements for your greyhound.
ACT - www.greenhounds.com.au
QLD - www.greyhoundpets.org.au
VIC - www.gap.grv.org.au
SA - www.gapsa.org.au
WA - www.greyhoundsaspets.com.au
TAS - https://dpipwe.tas.gov.au/racing/greyhound-un-muzzling-information
NT - Muzzling exemptions available.