We don't normally offer advice on elements of a centrelink benefits however- I googled "centrelink carers payment household" and it came up with this-
"The person you care for can be anyone, including a relative. It can be paid to more than one person in a household, such as a couple caring for each other".
As far as I can see you could be eligible for carers payment each. So I'd apply and see how you go.
Nothing binding in the above but happy to help out.