You ask a great question and it is important to know that you have a legal 'duty of care' to provide a safe place of work. Even though that place of work may now be at home.

This is tricky given that not only is there an increase in the likelihood of mental health issues but also Domestic & Family Violence.

I would strongly encourage you to set up an EAP or here is a free service offered by the Government here:
 

https://www.mybusiness.com.au/management/6830-beyond-blue-launches-free-coronavirus-support-service?utm_source=MyBusiness&utm_campaign=14_04_20&utm_medium=email&utm_content=1&utm_emailID=8c59beee9ef6e26c0186d326a3c73f29b6269400a7c8182655e708d9666991cb  

On the D&FV risk, if you suspect someone in your team is experiencing this then I highly recommend talking with Janine Lee from Domestic Violence Business Solutions.

Other than that keep in touch with your team. Look to reach out more frequently to high risk employees.

Also worth noting that my team and I are Mental Health First Responders and can provide you with advice in managing these issues.

Hope this helps, Natasha

Great advice here... You can also support yourself and your staff with their mental wellbeing by helping them understand what's actually happening - from a human behaviour perspective - by checking out www.social-wellbeing.com.

I've set up this platform to provide online courses to support during this weird time.  Short, 15-min videos that offer practical and useful content, to help you understand and overcome the Pandemic of Panic and the Lockdown Meltdowns...

Here to support you... xoxoxoxox

Great advice from Natasha, other things you can do to help yourself and your team:
Make sure people are taking breaks to stretch every 30 to 60 minutes. I would encourage you and your team to create a regime which includes excercise of some sort each day. A walk would do wonders for mood and general well being. There are many free resources for working out at home too. 
I use Fitness Blenders to help keep me in shape both physically and mentally. https://www.fitnessblender.com This of course depends on each individuals fitness and interest in exercise but it is essential to mental health as well as physical health. 
Ask your team what if any support they would like from you and in what form and do not be afraid to ask for support for yourself. As Natasha says there are a number of terrific free resources such as the Mental Health Line 1800 011 511. 
All the best to you and your team.

Thanks everyone. Great tips here. @Natasha Hawker @Sonia King @Anita Van Rooyen Do you know if there any online meditation and mindfulness companies that are offering online sessions to workplaces? 

Thanks @Natasha Hawker .  Just good to know of a few places. I think meditiation and mindfulness is very important - now moreso than ever during these times we find ourselves in.