If you have already cohabitated for at least one continuous year (and it sounds like you have between you being in Japan and her being in Canada) you are qualified as common-law partners and you should apply that way. The conjugal partner category is dicey - it's basically common-law with the cohabitation requirement waived because a couple
cannot live together and/or
cannot marry because of an immigration barrier coupled with threat of persecution due to the nature of the relationship. Because your gf is visa-exempt, and you have spent significant time in her country and she was able to come to Canada, too, AND because you could marry (even though you're choosing not to), you probably would not be successful with the conjugal route.
Keep in mind that if you apply as common-law partners (rather than marrying and applying as spouses) you have to prove both the one year co-habitation and your genuine relationship. Things like emails, phone records, pictures and proof of trips to visit one another all go towards proving that your relationship is "genuine", and not just entered into to facilitate her entry to Canada. The co-habitation requirement is another matter - they're looking for things that demonstrate that you have "co-habitated in a marriage-like relationship for at least one continuous year". Probably the best source for information about how they assess common-law qualification, and what information to include with your application to prove it, is
this CIC processing manual - Sections 5.34-5.36.
Also, even though she can't extend her working holiday visa - she could still apply to
extend her stay, and change her conditions to a visitor so she can stay for long enough (hopefully) for you guys to be able to qualify as common-law partners based on her stay here in Canada. For a reason, she can say that now that her working time is over, she wants to take some time as a tourist to see Canada before returning home - but she shouldn't mention the relationship with you. Just another six months will get you common-law qualification AND time to submit an application to sponsor her for permanent residence, and then she can apply to extend again based on the fact that you're in a "qualifying relationship" and she is being sponsored for PR.
You will need to get the extension application to CPC-Vegreville BEFORE the expiration of her WHV. That gives her "implied status" to remain in Canada until they make a decision on the extension (about 100 days). Track the mailing and get delivery signature confirmation - that will be her proof of "implied status", should she need it. Even if the extension isn't approved, by the time she'd have to leave you'll have met the common-law qualification and, if you can prove it, you'll be able to apply to sponsor her, even if she has to go back to Japan. Short separations - especially ones resulting from the foreign national leaving Canada when their authorized stay is over - are permissible.
Once you know for sure that you're going to apply to sponsor her, you'll need to make a decision as to whether you'll be doing it via the inland application process, or outland application process. Don't make the mistake of thinking that because she is in Canada with you, you have to apply inland. There are several drawbacks to the inland process that are not readily apparent if you're taking your information about it strictly from the CIC website. Let us help you make a determination about the best, most expedient route to a successful process before you jump in with both feet. In the meantime, get that extension application off to CIC, and then go from there.
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