Disclaimer: I am not a lawyer, this is just my personal exploration of the legal landscape in Canada and how it differs from that of the US.
The decision in R v Morgentaler (1988) is considerably different from that of Roe v. Wade. Where Roe v. Wade places considerable importance on the notion of individual privacy, R v Morgentaler places central importance on security of the person (although it does address rights issues in other sections of the Charter as well).
At the core of the Morgentaler decision is the Oakes Test analysis (described on pages 73-76), which concludes that what was at the time S251 of the Criminal Code could not be saved under S1 of the Charter. Oakes sets out a judicial review procedure for weighing competing interests (and as with all such things, there is considerable debate around it still). However, at the end of the analysis in Morgentaler, the basic conclusion is that the impact of criminal sanctions on the woman are hugely disproportionate to any state asserted benefit in the restrictions. It also takes apart any of the procedural / regulatory structures that stem from S251 as also being unreasonable infringements.
There is a good reason here that you haven’t seen any serious attempts by governing parties in Canada to tackle creating another law that specifically tries to limit abortion: It’s going to be really hard to create such a law that doesn’t end up failing scrutiny under any kind of review like Oakes. Further, any such law is going to find itself subject to challenge as unreasonably restricting the rights and liberties afforded to women while placing no restrictions on the male sperm donor.
This is a very thorny problem for any lawmaker to tackle, and potentially one that is intractable without major changes to fundamentals of law such as introducing the idea that a foetus has some legal standing.
Currently, Canadian law basically says that a foetus is considered part of the mother’s body until such times as it is “delivered alive from the mother’s body”. In other words, up to the point of live birth, the fetus is treated like any other part of the mother’s body and it is her decisions that are paramount. In other words, a womb isn’t a condo that some other party is renting out for 9 months.
There have been numerous attempts to change this by way of private member’s legislation. However, those bills have typically bubbled around for a few months or years until dying either on vote or when parliament dissolves for an election.
The reality of those bills, were they to be enacted, is that they would likely also fail scrutiny under Charter review. The problem that would arise with foetal rights legislation would be an entirely different set of challenges, because now you have two “persons” with competing rights. The anti-abortion crowd would of course argue that the foetus’ rights should trump those of the mother, but such things are not so simple in reality because the structure of the Canadian Charter of Rights and Freedoms places rights of individuals in tension with each other, with no one person's rights superseding those of another.
Were parliament to declare a foetus a "person", one opens an entire can of worms legally, and I suspect that what would emerge would end up right back where we are today.
Why do I say this? For several reasons, actually. First, any law which looks like some of the abortion bans currently tabled in US legislatures will collapse under Oakes. Second rests in our current approach to the law and children / youth. Current law approaches place responsibility entirely on the parents at the birth of the child, and gradually reduces that as the child becomes more able to take on responsibility. So, for example, if a toddler breaks a neighbour's window, we generally say "oops, that was an accident", and the parents are held responsible for the child's conduct. When a 13 year old breaks the neighbour's window, we're more likely to hold the 13 year old responsible for their actions, although we might look sideways at the parents for raising a hoodlum. Basically, the idea is fairly straightforward: as the child becomes more able to assert independent actions, we grant them greater responsibility.
At birth, a child is able to breathe, and take sustenance independently of the person who birthed them, but is still largely dependent upon the parents to survive. That level of dependency grants the parents absolute control over much of the child's life as long as they protect the child's health and well being. When the child is 18 or older, we deem that the child is now capable of being fully independent (I'll ignore emerging evidence from developmental psychology in this matter for now).
I would expect that means from a legal perspective, you would end up back where we are today because the dependency of a foetus (and its antecedent forms of zygote and blastocyst) are entirely dependent on the person carrying them in all respects. The pregnant person is not only responsible for themselves but the developing being inside them at that stage. The developing being has no ability to assert or exercise rights in any legal sense, nor can they act independently. That returns us to the state where not only is dependency absolute, but the risks associated with pregnancy are borne by the same person. Therefore, one can reasonably assert that absolute dependency, along with shared risks grants absolute control over decision making to the person most able to make those decisions objectively.
Anti-abortion people will howl about "fetal heartbeats", and "viability" thresholds, but those are much harder to establish than one would first expect. What is often called a "heartbeat" is actually little more than a bundle of neurones acting autonomically. There is no "heart" formed at that stage, merely the potential for one to exist. Viability is a similarly difficult thing to establish. We can look and say "well, there's a well-formed foetus present", but whether or not that particular individual is viable at the moment of examination is a matter of probabilities, and available technology / medical methods.
Then there are the risks associated with pregnancy. They are many and a blind enforcement of "the law" to regulate pregnancy places women at risk. It has happened before, and it will happen again in the US.
There can be a myriad of exceptions, and creating arbitrary lines based on a calendar in something as complex as gestation is a bit of a fool's errand. This is why abortion needs to remain a matter of medical ethics, rather than a matter of law. Even if we could make a reasonable argument for foetal rights, the fact is that law is far to blunt an instrument to use here.