If you are a sole trader or business owner working from home, the best way to determine what you can, or cannot claim is to go straight to the Australian Taxation Office Website to get all the facts. Too many ask friends, online gurus who are not tax practitioners to save money paying a tax or BAS agent. 

Running your business from home 
https://www.ato.gov.au/General/property/property-used-in-running-a-business/running-your-business-from-home/

If you earn under $60k a year, you can obtain FREE advice from the Australian Taxation Office to submit your tax return. 

Tax Help Program
https://www.ato.gov.au/Individuals/Lodging-your-tax-return/Tax-Help-program/

Check out the ATO's Factsheets for easy reference according to your occupation
https://www.ato.gov.au/Tax-professionals/TP/Tax-Time-Toolkit-general/?anchor=OccupationGuides

What can I claim?
There are TWO options available to you at the current time to 30 June 2020. 
1. Claim your deductions from your receipts (ensure you split personal vs business percentages)
2. 80 cents an hour - This is a flat rate where ALL expenses are inclusive.
This means you cannot claim .80 cents a hour and the new laptop, internet & phone. As ALL expenses regardless of their value are included in the flat .80 cent per hour rule. You do need to have kept a diary or provide a time sheet to substantiate your claim.

TIPS FOR THE NEW FINANCIAL YEAR 
Use the ATO FREE app for the new financial year 
https://www.ato.gov.au/general/online-services/ato-app/mydeductions/

Pay a registered Tax Agent (Whose services are tax deductible)
Ensure you check that they are registered by typing in their details on the Tax Practitioners Board website
https://www.tpb.gov.au/registrations_search

Hi @Hatty Bell 
Not quite.
To claim utility bills - you need to have a set area (not used for personal use) where you work. This area needs to be measured as a "percentage" against your personal use areas.

For example, you live in a three-bedroom unit, but allocate one of the smaller rooms as your "working space". 
After measuring up the square meter of the unit, you discover the third room you use is only 10% 

10% of your utility bill can be claimed on your tax. This process is fine if you rent, but gets more complicated if you own the unit, as you will now lose a percentage of your capital gains exception on the sale of the property.  

As you can see it gets very complicated.

Any furniture you purchase must be 100% for business use to claim the total amount also.
The ATO requires a diary for all hours worked to substantiate the deduction.

Phone/internet and mobile phones require a 4-week diary to be kept and apportioned accordingly.
See https://www.ato.gov.au/Individuals/Income-and-deductions/Deductions-you-can-claim/Other-work-related-deductions/Claiming-mobile-phone,-internet-and-home-phone-expenses/

Normal living expenses cannot be claimed - even if you do work from home. 

That is why the 80 cents per hour ruling is so attractive