Taking a matter to court does not halt a statutory fee or charge. Since it's not from an existing court decision, a stay is unlikely to be available to you.
You could find whatever mechanisms are available in your state along the lines of waiver/hardship. For example, here is Queensland's:
Quarantine fees and payment
Alternatively, your options are probably along the lines of:
- Write to them and ask if they will not take action to enforce the debt until the application is dealt with;
- Apply to the court for an interim injunction to stop them from taking action until your application is determined - I do not suggest that this is a 'do it yourself' proposition in any way; or
- Refuse to pay it, wait to see if they take action against you, and then seek to join the two actions together.