If you were to sign the agreement now, it would be under duress because the other party is basically forcing you to do so. Parenting plans signed under duress are considered void, and it would be prudent to write "signed under duress" near your signature of you did decide to sign it now.
When you file your initiating application with the court, make sure you also tick the box and apply for interim orders. Interim orders are what the court puts in place while proceedings are under way as proceedings can often take a year or two to reach completion and it's not often in a child's best interests to stop spending time with a parent for such a long period.
For interim orders, it's prudent to keep them fairly simple - for example, that the parents have shared parental responsibility, that the child live with the mother (I assume), that the child spend regular time with the father (such as alternate weekends from after school Friday to before school Monday and an overnight each week). Also include half gazetted school holidays and special occasions (Christmas, birthdays, Father's Day). Anything outside the 'standard' orders - parental responsibility, live with and spend time - can probably be held over until final orders.
Provided there's no issues of family violence or risk to the child, the court will give interim orders facilitating the child's time with you.
Be patient while you wait for your first interim hearing. The court frowns upon parents who take justice into their own hands, so just be patient, keep the child's exposure to conflict to a minimum and treat the mother with respect so that any allegations she might make about you are at no time substantiated. Let us know how you go.