I have clients with 10 IP's but not purchased in 10 months, more like 5 years or longer and none are single mums.
You need 2 basic things before you can build a property portfolio, savings and/or equity to fund the minimum settlement funds needed and to be able to show the income for servicing of debt.
If you buy very well and structure your finances well, it may be possible.
Most would need to release equity in their own home first to cover the funds needed to settle on the subsequent purchases. You may then consider what type of IP's to buy, it may be lower cost IP's in regional towns or look at lower stamp duty IP's (off the plan in Vic perhaps) and higher loan to value ratio (LVR) loans with selected lenders in order of lowest serviceability first.
You may need to structure your purchases also based on rent yield to cover the issue of servicing unless you have high incomes. Manufactured growth (renovations etc) are a way to increase rent yield and value but it takes time and money.
My personal view is that 10 in 10 months is not feasible for most, to be able to do due diligence, arrange finance and the settlement, getting tenants etc. I have also been to the sales companies that promote their ability to do this, mostly I take away some bits of information I may not have heard before and then steer clear of them after that.
Why put yourself under the pressure to do this?