To do your own bookkeeping as a business owner you don’t need to enrol in an official bookkeeping and accounting course. Learning by doing is definitely the way to go for most people (and you’ll be surprised at how quickly you pick things up), but it definitely wouldn’t hurt to brush up on your knowledge of key bookkeeping terms and concepts by completing a mini-course.

If you use accounting/bookkeeping software, most software providers have amazing resource hubs to help you learn how to get the most out of the feature and tools including find how-to guides, troubleshooting, FAQs, video tutorials and more.

From our research, below are some of the most popular bookkeeping courses for small business owners: 

Coursera: Financial Accounting Fundamentals offered by The University of Virginia 

• This course will teach you the fundamentals of financial accounting including the three most commonly used financial statements (balance sheets, income statements, and cash flow statements) to equip you with the basic skills to prepare and analyse your business’s financial health. 

• Cost: Free

LinkedIn Learning: Accounting Foundations: Bookkeeping 

• This course helps you understand the four key steps in bookkeeping: analyzing transactions, recording the effects, summarizing the effects, and preparing financial reports.

• Cost: $40.90

• Study mode: Online 

The Career Academy: Introduction to Bookkeeping 

• This online course teaches you the fundamentals of bookkeeping including how to balance the books, invoicing, payments and cashflow management. The course is also a Xero Education Partner with Xero Learn. 

• Cost: $197.50 + GST

• Study mode: Online

Realistic expectations for learning bookkeeping
As a business owner some of your hats are:
Manager
Marketer
Debt Collector
Worker
Administration Clerk
Receptionist

I feel the real question is to ask are you better served to do your own bookkeeping?
A bookkeeper will cost locally $55 plus per hour depending on the duties you need them to perform.
If you are earning more than that an hour, wouldn't your time be better served "making money" per hour instead of doing the bookkeeping?

If you already own your own business, do you have the time to do a bookkeeping course?
I would seriously doubt it. 

Decide on what you need to do the bookkeeping....
Sole trader / trust / company turning under $75000 year not registered for GST
Use the ATO MyDeductions app for free
No bookkeeping training needed, just record the income / expenses through the year
Before you need to do your tax - download the excel from the app and email it to an accountant or add it up and call the ATO's free tax service to fill out your own tax return if  it's really simple. 

Registered for GST, you are far better to decide on an accounting software
Online is best, as you can use it on your smartphone, tablet, laptop or desktop. 
Go to the software advisor's area and search for a specialist in your area
Pay for them to set it up "correctly" and then train you on how to do your own bookkeeping on a day to day basis. Cost should be around $500 max for both. 

Atternatively, pay them a few hundred to set it up right, then go to youtube or the software's website to learn how to use their product. 

There are a few practical options for you to explore and think about.