Can a small brewery stand down its staff for COVID-19?

At this stage, the general answer is No.

But you are in a good position to negotiate an agreed stand-down with employees - particularly if they have been with you for less than 12 months, or if you employ fewer than 15 people.

An employer can only stand down non-casual employees without pay if there is a stoppage of work for which the employer cannot reasonably be held responsible and the employee cannot otherwise be usefully employed.  (For casuals, you can simply not roster them on.)
 
Historically, a downturn in business is not considered a reason which is beyond the employer's control. For example a cineman chain or gym ordered into shut down by the government. Other examples where a stand-down is justified might include an interruption to supply chain or destruction of machinery or work premises.

But as of today (24 March), when pubs (and tap-rooms) are closed except for take-aways, but not breweries, it would only be your staff who are only involved in serving the public on premise who are affected.
 
There is no case law on the subject which deals with a public health emergency of the current scale. While it might be arguable that circumstances are beyond the control of the employer, there is no confidence at this stage that the argument would succeed if the matter were brought before the Fair Work Commission until a business is actually on a list published by the government as those who must close. Looked at harshly, there is nothing, other than dire economic circumstances, stopping the business from continuing to operate.
 
That said, in the event that the FWC is called upon to deal with these matters, you would hope that members of the Commission adopt a pragmatic approach. Case law from times of war suggests pragmatism often triumphs over black letter law. The likely worst-case scenario is that the employer would be required to pay the employee normal salary or wages for the period during which they were stood down. A penalty for contravention of the Fair Work Act is also a possibility, but it’s doubtful that even regulators would have, or be willing to use, the resources necessary to litigate those matters.
 
So the current advice to employers is to negotiate with employees for them to take leave with or without pay. In the event of a stand-down without pay, the employment relationship continues and leave entitlements continue to accrue [i.e. a benefit for an employee, compared to being retrenched, with no guarantee they will get their job back later]. It also appears that Social Security benefits are being made available to employees who are stood down, but remain employed.
 
The alternative is, of course, to make the employee redundant. That would require immediate payment of any termination benefits, though in the case of:
(1)  an employee with less than 12 months service; and / or
(2) if you are a “small business” which employes fewer than 15 staff,
there is again no obligation to make a redundancy payment.

So if you are in that situation, you are in a much better position to negotiate for your affected staff to agree to be stood down.

By the way, we don't do employment law here, so thanks go to my good mate who does - Pete Vitale at https://www.petervitale.com.au/