I am a PhD graduate in Analytical Chemistry in Australia, searching for a job.
I don't have proper idea what are the job positions we can apply except postdoc or lecturer.
I would prefer to join government/public sector job. Can you guys please help me?
I just went through some public job websites, where I only find jobs related to administration, IT....

I think you will find that a PhD is less appreciated outside of academia.

However, you can definitely find a career path beyond academia. You may be reporting to a Bsc or MSc holder.

You can check out articles such as https://cheekyscientist.com/top-10-list-of-alternative-careers-for-phd-science-graduates/ for ideas on what else is out there. You don't need to join Cheeky Scientist to read their other articles. Until you narrowed down on the type of role you want, you won't be able to do a good search on job sites.