The skills assessment is required so you, the migrant, can apply for an Australian visa and work in Australia as a Hairdresser. This is the way Australian Immigration can gauge if you are in fact a Hairdresser under the Australian guidelines.
Many people want to move to Australia as a Hairdresser and without a skills assessment delivered by an approved assessing body, Australian immigration have no way in checking a migrant has the necessary skills.
To emigrate to Australia as a Hairdresser you will need to complete the Hairdresser skills assessment for a skilled visa.