FTB isn't paid to the primary carer - it's paid to the family, so can be in either name (and is best kept in one name for the life of claiming - swapping and changing is right painful)

PB, the info you've given is not correct for this circumstance
you've provided the information that applies if BOTH parties are on income support, one of those parties being on a pension (aged pension, carer pension, disability pension) - they income is treated differently in these circumstances (due to the theory that pension customers have less ability to earn money so the income is split as if earned by both parties, and the impact is different. basically if your partner is on one of these payments, you can earn more before they lose the entire payment.