All travel insurances are the same in this regard: you need to check the policy detail for travel disruptions. Pretty much all of them cover missed connections but with different details included. They don't really depend on how you've arranged you ticketing but some do spell out expectations on the duration of your connections and how much the incoming flight needs to be delayed for the cover to apply. One that comes to mind immediately is minimum 4 hours in between the flights and the incoming delay needs to be >90 mins to be eligible for cover.
Though, already for your own peace of mind and certainty, it'll be good if you left a day between the connections just in case your first flight AU-SG is cancelled and you're rebooked for next day (or the original flight is heavily delayed).