Under no circumstances can you move permanently to Canada until you have permanent resident (PR) status. Once you have permanent resident status, THEN you can move in and bring your furniture. In the meantime, you will need to leave it in the U.S. with a friend or relative or in a storage unit.
Step 1: Come for a visit to Canada and get married. You will need to prove that you are only coming temporarily. Alternatively, you could get married somewhere else, but it sounds like you are a gay couple which may limit where you can get a legal wedding performed.
Step 2: Fill in all the forms and gather together proof of how your relationship developed to show that you are a genuine couple and not two people who just got married for immigration purposes. For some people, it can take 2 or 3 months or more to get everything together. You will need a marriage certificate, which probably can't be obtained until the marriage registration is processed by the province. One more thing while I think about it, if you get married in Quebec there is a 20-day delay between getting the marriage license and actually getting married. You need to pay at least $550 of the fees and send in the application.
Step 3: After 1-2 months the sponsorship will hopefully be approved and you can apply to Quebec for a Quebec Selection Certificate. The fee for this application is $250. An outland application through Buffalo, NY, is the fastest. So, the application then goes to Buffalo and you need to wait another 4 to 10 months (or more or less) for them to process it. If they need more information, there may be an interview in the U.S., probably in Buffalo or New York City.
Step 4: Once Buffalo ask for your passport, they'll put the PR visa in your passport. Then, you have to "land" in Canada. This is usually done at a border crossing coming into Canada. If you're in Canada at the time, you need to cross the border and then come back. You can bring your furniture and all your belongings at that time or bring a list of them to be physically delivered or brought in later. All your stuff, including your car, is duty-free as long as it's in used condition.
I'm assuming that you no longer will have house or apartment in the U.S., but if you come for a visit, you need to have a permanent U.S. address. You also have to show that you have "ties" to the U.S. that will compel you to return after your visit (at least if the PR might not be approved). Ties might include a job to go back to, property that you own, relatives that you have to look after, money in the bank, any kind of obligations. If you can't show that your ties to the U.S. are stronger than your ties to Canada, they will be reluctant to let you come at all, even for a short visit, because they'll be afraid you'll stay permanently, even if it's illegal.
It sounds like it might be hard to prove sufficient ties to the U.S. in your situation, but if you are able to, you can visit for up to 6 months, or whatever shorter time period they may give you. Once you're in Canada, you can apply for an extension to this time period, and if you've applied for PR or are at least well on the way to completing the application, an extension is likely to be approved for however long they think it will take to get an answer on the PR application. You can't work or go to school as a visitor to Canada, so you'll need to show how you're going to support yourself during the visit without working illegally. If you're short of money, you'll need your fiancé to show that he is the source of that support.
The tricky part is that you're not married now, so you're not eligible to apply yet, but proof that you're preparing an application (especially a receipt showing that the fees are paid) will add credibility that you're not planning to immigrate illegally. You need to plan this out very carefully or it won't work at all.
That's long, but it's really just the basics. You can send me a private message with more details if you want more detailed information.
Isn't that what the US is trying to stop the Mexicans from doing. I am sorry of I am coming across slightly blunt but with all the info out there, you obviously have internet access USE IT!!!