Under Malaysia's Animal Welfare Act 2015, every individuals and businesses who handle animals for a living are required to apply for a license from the Animal Welfare Board. If you are a pet owner, you will have to check with the local council of your own area as by-laws on pet licensing differ from one location to another.
It is also a requirement from MSIG that your dog has to be licensed by your local authority. This could be with your local council such as DBKL (for Kuala Lumpur), MBPJ (for Petaling Jaya), MBSJ (for Subang Jaya), MBJB (for Johor Bahru), Penang Island City Council and others.
For pet owners living in Kuala Lumpur, you can apply for a dog licence easily via DBKL's online portal. Similarly for pet owners living in Penang, you can also do the same via MBPP's online portal.