Airside transfer is very limited in Dublin, it’s only possible if you both arrive at and depart from Terminal 2 (and a few other conditions which I don’t remember).
All passengers arriving in Terminal 1 will have to go through passport control (including those arriving from the UK despite Ireland and the UK being part of the Common Travel Area).
Just after passport control in the baggage reclaim hall there is a passageway towards departures.
So you should budget quite a bit of time for the passport control queue and processing. I believe you’ll also go through security, but that would most likely have been the case even if there was airside transit. No idea if you get through the normal security check-in (and it's sometimes a very long queue) or if you benefit from a shorter queue here.
Also, even if online check-in is possible, that does not mean you will necessarily get a boarding pass in all cases. There is always a risk that for some reason they will ask you to go to check-in to get your boarding pass (usually to check documentation). This is very often the case for flights to the US for instance, don’t know about flights to Canada. In that case you would need to get to departures and to the check-in desk before the check-in deadline.
While if all goes well even this last scenario is perfectly doable in less than 3 hours (probably a lot less), with a self-transfer you have to remember that if you miss the gate closing time (or, if you have to go to check-in, the closing time of check-in desks, usually much earlier), you will be considered a no-show.
While the details vary with the airline and even more with the type of fare, in many cases that means your ticket will be cancelled, and often any further flights on the same ticket will be cancelled as well (this is more frequent with traditional airlines than with low-cost airlines, no idea where WestJet lie on that matter).
This means booking and paying for a new ticket at the last minute, at last minute prices, often a lot more expensive.
Also, if that new flight is the next day, any hotels, meals and transfers to/from the airport are on you.
If the second flight had been for a short, cheap (even at the last minute) and frequent flight (like flights between London and Dublin), then it would be no issue to consider your ticket for the second flight as “throwaway”. Here the risk is quite a bit more significant, so you should probably have quite a bit more buffer.
Also remember that in addition to possible delays (or last-minute cancellations), there is also the risk that either airline will change the schedule of their flight, and that could make the connection even more risky or even outright impossible.
