Hi Vick,
First of all congratulation. One question only, Is there any date given on the visa that holder need to enter Australia by so or so date?
Now coming to exemption, You can apply for one using the link given below:
https://travel-exemptions.homeaffairs.gov.au/tep
Now few points when you apply,
Choose critical skills category,
Provide evidence of her experience in nursing sector. You can add her assessment of skills if you have procured. You can also add her experience letter. Apart from that you will need to provide few more documents like her visa and passport details etc. You can find required document in Immigration department website. Look for Travel Restrictions in website.
In explanation, Explain how she can be helpful in pandemic situation in Australia by providing front line services immediately after arriving to Australia.
Also explain that you need her here to support you after being separated for a very long time.
You might not get exemption on the first try. Keep trying, your wife being Registered Nurse there are very good chance you won't have apply for too many times. Every time you apply just add some more details and add some more emotions that you feel.
If you need some more help let me know.
Good luck,
Jay