Yeah, do it! I think crossing Canada in 3 months is a good amount of time, I think if overall if you average 2000 km in a month you can cover a lot of ground, but still take off one to two rest days a week.

The only change I'd suggest is going the other direction, Vancouver - Halifax, going west to east. The prevailing winds are that direction, so it would probably make things a bit easier. Not saying you're going to have a tailwind every day, but overall, it will make a difference. And fighting the wind sucks - nothing makes a day of touring more frustrating, in my opinion. I know, it would be nice to finish with a good downhill into the lower mainland, rather than cross the Rockies in your first week or two - but when you're crossing the prairies, it might be worth it.

But have fun! Do it.