A relative of mine in Australia has been in touch with someone from Centrelink.gov.au about ways I could get permanent citizenship in Australia. This person suggested that one route would be to come over on a one year working visa, get work in my required field (Computing) and then apply for the visa to become permanent once I had work.

I have been looking through the Visa options and requirements on immi.gov.au and can't see how this is possible. Has anyone ever been able to get work on a working visa and then successfully apply for permanent residency based on their current employment?

First of all centelink deal with social security payments and not visas ! They are not qualified to give advice on visas !!

What you have been told is mainly rubbish !

However what could happen is that while you are here on a WHV, you could try and get an employer to sponsor you via the Employer Nomination Scheme (ENS) providing you and the employer meet all the requirements.

It wouldn't be based on your current employment as such but if the employer had employed you on the basis of you having a WHV and then wanted to keep you they could go down the ENS path. You would also of course have to fulfill all the requirements of the WHV while you are there also.