Canadian law, as currently understood, would not give this contract any force. The issue, we are told, is the "best interests of the child. (Except when it is the absolute autonomy of the mother. Canadian law is a bit confused, actually, but it pretends not to be.)
Ms. Doe has argued that this position violates s. 7 of the Charter. So far, she has obtained no support in judicial circles, although her argument surely follows from basic principles of autonomy. There can be no doubt of Ms. Doe's right not to have a legal father for her child if she were willing to live alone. Why shouldn't she be able to have a man in her life? Even the impact on the child's welfare is unclear once we take incentive effects into account. (I realize that our courts hate doing that.)
It is hard not to have a smidgin of sympathy for the position of Alice in Whit Stillman's The Last Days of Disco, although we must in the end admit that Charlotte has the better sense of our fate:
Alice: I’m beginning to think that maybe the old system, of people getting married based on mutual respect and shared aspirations, and slowly, over time, earning each other’s love and admiration, worked the best.
Charlotte: Well, we'll never know.
*Currently being as of May 30. I am too lazy to check to see if leave has since been granted or denied.
**Shouldn't that be Mr. Roe? Ms. Doe doesn't sound like the type to take her spouse's name.