There's too many facts missing to predict an outcome (and it's impossible to predict anyway because it's dependent on the judge and the other party's case as well), but of course it is possible. He would have to show it's in the best interests of the child to spend equal time with each parent according to section 60CC of the Family Law Act 1975.
Where the court upholds the presumption of shared parental responsibility, it must first consider if equal time arrangements would be in the best interests of the child, and where they are not found to be in the best interests of the child, it must then consider if orders for substantial and significant time are in the best interests of the child.
Substantial and significant time consists of a mix of weekends, weekdays, holiday time and special occasions, like birthdays, etc. Typically, an alternate weekends arrangement isn't favoured by the court anymore, so even if equal time isn't awarded, the other parent has a good chance of gaining more than what he shares with his child now.
There are no compelling facts listed here which suggest an increase in time is not in the best interests of the child, either. Not working doesn't make a person a bad parent, and treating the child like a toy is an opinion, not fact. Further, there's a hundred different ways that the facts listed here could be used to the advantage of the other parent, like arguing the child's time with her dad must increase to enable her to continue having a meaningful relationship with him because her relationship is not otherwise receiving any support while she is not in his care.
So, in summary, yes, it is possible for him to gain equal care, but it depends on how you pitch yor respective cases, what the facts of the case are, who the judge is and whether or not such an arrangement would be considered by the court to be in the best interests of the child.
