Hi Kate,
Welcome to the forum.
I haven't gone through this process (yet

) but I did start to look into it.
You have to be willing to support your parents for 2 or 10 years and provide Assurance of support.
Here is a link to parent category visas (if they are outside Australia) :
Family - Visas & Immigration
And here is the link to the Assurance of Support:
Australian Immigration Fact Sheet 34. Assurance of Support
I remember that the person (or people) doing the sponsoring have to be earning a certain amount of money - which I can't find at present.
I would check with an agent (or an immigration department) since they may be able at what stage during the visa application you could leave your job.
Will your husband still have his job? If so maybe you could both sponsor your parents?
Regards,
Karen