Australia
Each state and territory has public-health legislation covering 'skin penetration' businesses, with infection-control standards, notification/registration of premises to the local council, and council inspection. Requirements for operator training vary and are generally less prescriptive than the UK's, but the hygiene obligations are enforceable. Advertising is subject to consumer law and, where health claims are made, therapeutic-goods rules.
Canada
Provinces and their regional health authorities issue and enforce personal-service-establishment / body-modification regulations and infection-prevention guidelines; municipalities may add licensing. There is no single national practitioner certificate. Health Canada regulates cosmetics — including tattoo and PMU inks — under the Food and Drugs Act and the Cosmetic Regulations, maintains a Cosmetic Ingredient Hotlist, and has issued advisories and recalls on contaminated or non-compliant inks.
Bottom line
In both countries, find the local health authority for your address, meet its skin-penetration/infection-control standard and premises registration, keep pigment and client records, and use only pigments that comply with the national cosmetic rules.