You're right, there is no short term visa for spouses of Canadian citizens. She should apply for Permanent Residency.
There are two streams of PR applications - "Inland" and "Outland". Inland means the application is processed in an office in Canada, and the applicant is IN Canada, and must remain in Canada for the entire duration of the procedure, which may take 2 or 3 years. (Every time she leaves Canada, she risks having her entire application cancelled. That means that until she gets PR, which may take 2 or 3 years, it would not be advisable for her to leave Canada for any reason, including emergencies.) "Outland" means her application will be processed in Manila, as all Japanese applications are sent there. Manila has a "processing time" of 15 months or so. The definition of "processing time" is how long it took them to finish 80% of applications. The median seems to be well under a year. How long it takes depends on the application. Things that cause delays are, for example, incomplete application, outdated or incorrect forms, missing signature, criminal record, suspicion of marriage of convenience, lack of proof of your relationship, child(ren) from a previous marriage/relationship, etc. I would also add that Japanese and Korean citizens seem to be processed faster than Philippino applicants, because there are less cases of immigration fraud from these countries.
As a Japanese citizen, I would say your wife should apply for Permanent Residency "Outland". Note that you can be physically present IN Canada while applying Outland. "Outland" is just the name of the category your wife will be applying, not whether she is in or out of Canada.
If your wife is planning to come to Canada in April, try to get all the paperwork done before that. Read the guides on the CIC website - including the guide for Japanese citizens. That will give you a big list of documents she needs to send, and most of those documents are easier to obtain while she is in Japan. She can apply before she comes to Canada in April. Or she could send the application after she arrives. Just remember that documents such as her police certificate are valid for only 3 months from date of issuance, so don't let them expire.
I applied for PR Outland almost exactly a year ago, in February 2014. I then came to Canada as a "visitor" in March 2014. At the border they did not ask many questions, and I said I was visiting my husband. They did not stamp my passport, meaning that I could stay in Canada for 6 months as a visitor. In August 2014, I applied online for an extension of my visitor status. I asked to stay until September 2015, and it was granted. I got PR in early October 2014, and went to the US for a few hours and re-entered Canada as a Permanent Resident.
Manila took about 7 months to process my application. I think it would have taken much less, if they had not asked me to provide a second police certificate, which took 2 months to get.
While your wife is here as a visitor, she cannot work or study. Whether she can get provincial healthcare or not depends on the province. But if she applies Outland now, she will probably be a permanent resident by the end of the year. If she applies Inland, after 4 months she can get an Open Work Permit, which enables her to work while she waits. However, it may be a very, very, very, long wait. I would advise against applying Inland. Inland Might be beneficial for people who need a visa to enter Canada. As a Japanese passport holder, your wife can come and go as she pleases, more or less. She can stay here with you while her case is processed.
You can send me a message if you have questions.
