All of the above is the correct pathway for getting time with your daughter, but there are some things you should understand to help with your decision making.
First, there are no rules or rights pertaining to parenting while ever there are no Court orders in place, so you and mum can do whatever you want for now. The way to resolve that problem of there being no rules is to get parenting orders in place as soon as possible. Refer to the post above on how to get that process rolling.
Second, if you and mum can't cooperate or agree on anything, and you do end up asking the Court to intervene, it will follow the Family Law Act in order to make its decision.
This is to your benefit for a number of reasons.
The Family Law Act says children have a right to know, spend time and communicate with both parents on a regular basis insofar as their best interests are met and regardless of whether their parents are married, separated, or any other denomination of a relationship status.
That's the first thing you need to understand: your daughter has a right to a relationship with you. You don't have any rights, per se, but she does.
The Family Law Act also says that the children's best interests are paramount in all matters heard by the Court. Section 60CC of the Family Law Act provides the Court with the issues it must consider to determine what's in a child's best interests. The primary considerations are the benefit to the child of having a meaningful relationship with both parents, and the need to protect the child from harm caused by abuse, neglect or family violence. There are also about 12 other considerations, but I encourage you to Google section 60CC of the Family Law Act to read through them yourself.
That's the second thing that goes in your favour. Except if you pose an unacceptable risk of harm to your daughter, then the Court will uphold that it's in her best interests to have a meaningful relationship with you.
The Family Law Act also asserts that shared parental responsibility is presumed, meaning you and mum have equal say about the major long-term decisions affecting the child's life unless there's an order in place that takes parental responsibility away from one parent and allocates it solely to the other.
That's a third point of benefit to you: you have equal say until the Court says otherwise.
In respect of care arrangements for the child, where shared parental responsibility is not rebutted, the Court must first consider if equal time is best for the kids, and failing that, if substantial and significant time is best. Substantial and significant time comprises a combination of weekdays, weekends, holidays and special occasions.
So, unless you live a decent distance apart, the concept of making a dad into an every other weekend parent is pretty much dead in the water in Australia. However, given your daughter's age, this is where it gets tricky.
Right now, an equal care arrangement is going to be inappropriate because the child is really too young, but the Court will still want the child to spend time with you, so you'd be most likely looking at an arrangement for substantial and significant time.
Most psychologists agree that children of tender years should spend time less time more frequently with each parent, rather than longer periods more frequently, since they lack memory and can experience anxiety if separated from a parent for too long. So, you could probably aim for perhaps an overnight or two every couple of days with incremental increases in the child's time with you until it reaches five or more nights a fortnight (plus half holidays and special occasions).
So, when you attend mediation with your ex, that's what you should propose as suitable care arrangements, because in the absence of risk, that's potentially what the Court will consider to be suitable care arrangements.
If she agrees, excellent. If she doesn't, which is the more likely outcome, then file an initiating application with the Court.
The law supports kids to have a relationship with both parents. Remember that, and don't do anything stupid to give her reason to seek an AVO. It complicates things in family law.