The question as phrased, the answer is no. It is not legal. If the 16 year old engages in any sexual conduct with the 13 year old, they could face statutory rape charges and the parental consent assuming there was any would have no bearing

Is it legal for a 13 and 16 year old to date?

In New South Wales, the age of consent is fixed by law at 16 for both heterosexual and homosexual sex. It is important to understand that it is not a crime for children under 16 to have sex! The law criminalises people who have sex with under-16-year-olds.