Interestingly, a judge asked my partner and father of one this exact same question, and the answer is none - you have no rights as a father under the Family Law Act 1975. Only the child has rights.
Those rights, however, are significant. Your child has a right to be cared for and spend time with both parents on a regular basis.
This is by no means legal advice, but more of an FYI.
First, everything - EVERYTHING - MUST be in the best interests of the child. "Best interests of the child" is a line you may want to get used to saying.
Second, courts first consider whether or not shared parental responsibility is in the best interests of the child. This affects whether both, or just one of you, will make decisions affecting the long-term care, development and well-being of the child, such as schooling and religion.
Third, where shared parental responsibility is found to be in the child's best interests, the courts then consider whether it is in the child's best interests to have equal shared time with each parent.
Fourth, if the presumption of equal shared care is found not to be in the child's best interests, then the court considers whether it is in the child's best interests to spend substantial and significant time with the non-resident parent. This means a mixture of weekends, weekdays, holidays and occasions significant to the parent and child.
The components that impact these decisions are things denoting 'reasonable practicability', like how far apart the parents live from each other, how well they can communicate, etc.
Of course, it is best to avoid courts all together, but I provide this information because it be of assistance in your own mediation attempts. It may help develop a better objective and a better pathway to achieving that objective outside of court through negotiation. Just remember the magic words - the child's best interests.