I agree with ariell. You can only count since June. You are required to live together continuously for one year. You may be allowed brief times apart, for example if you needed to leave town on a work trip for a few days.
The 3 weeks in Ireland and the fact the the lease was signed before your gf arrived help to show that you're not just in a "relationship of convenience" but they can't count towards the 1 year, unfortunately. The 3 months apart has to be considered more than a "brief time". Your wording also kind of gives your status away. You were "staying with her" in Ireland, not living with her. It just sounds like a visit.
If you come to Canada for a brief visit, you will usually get 6 months permission coming from a visa exempt country, but you have to be able to satisfy the officer at the port of entry that you are only visiting and that you are able and willing to leave Canada when your time is up. Things like a job that you have to get back to or an apartment back home that you're renting are important indicators that you won't just stay in Canada permanently. In short, you have to show significant ties to the other country.
Additionally, they want to be sure you will not work illegally in Canada, so you need to show that you can pay your expenses during your trip to Canada. In your situation, I expect that your gf will be supporting you, but if you tell them that, they will think that you don't ever want to leave.
If you will have applied for PR, that might be sufficient reason for them to let you stay, but you don't qualify yet for that, so I don't see that working, and you'd still need to show significant ties to return to.
I think your best bet is to come for a short visit (maybe 2 weeks or something) when your U.S. work permit expires. You'll need to show proof that you're on your way back to Ireland (or to some other country) when the 2 weeks is up.
Then if you get at least 3 months on your passport, you'll be able to file the PR application before your visitor status expires. If you can at least show that you've paid the fees for the PR application, there's a good chance of getting an extension at that time. (You're allowed to remain in Canada under "implied status" while awaiting a decision on the extension. It's been taking 65 days to process these as of Dec. 8/09.) So long as you're still legal, you can change your mind about the 2 weeks visit after you get here and stay longer.
Whatever you do, you can't lie to the immigration officer. The tricky part is going to be proving that you have significant ties to Ireland to return after your visit.