I know this is an older post but I just wanted to chime in and say that we have flown into Canada with our own 3 dogs and have had no troubles at all however the planning and filing of the eAPIS, getting your decal etc is a little more intesive and time consuming then your domestic flight planning. Another thing to note is that if you are renting an airplane, you may want to get a letter from the owner stating that they have given you permission for fly the airplane across the border. We were flying a club plane and did this.
Requirements for transporting animals is going to be different depending on the type of animal so be sure to check that out as I know there are quaratine requirements for some (like birds).
We checked into the requirements for transporting an animal such as a dog across the border and the main requirement for dogs over the age of 8 months was that they had a valid rabies vaccination as the US is not recognized by Canada as a Rabies -free country. If they are under the age of 8 months they have different requirements if they are not travelling with their respective owner. Here is some great info on trasporting dogs into Canada:http://www.inspection.gc.ca/english/anima/imp/petani/canine.shtml
I was concerned when we first flew the dogs in our own plane because I have relatives who frequently fly to and from the US from Canada on commercial airlines with their dogs. Commercial airlines have way more health certification requirements regardless of the dogs age when transporting them period, be it domestic or international. Thus it may be easier for GA pilots to do the transporting!
Also, be aware that certain provinces and municipalities have breed bans, specifically bans against pitbulls. The Province of Ontario has a pitbull ban.
For us, customs was a breeze both coming into Canada and Coming back into the US, however this can vary so be prepared to answer questions, fill out forms and sometimes have the airplane searched. You are also required to stay in the airpane until a customs official comes to the airplane to clear you so make sure that you have a way to keep the animals cool or warm depending on the weather. We came into Canada though Piney Falls on the boarder of MN and MB and then came back into the US through Nebraska and had good experiences both times.
I would maybe make the suggestion to Pilots that if you are planning a trip to Canada for vacation and have some room on your airplane, maybe consider seeing if there are any animals that need transportation into Canada! I have known people in Canada who have rescued dogs from the US, especially when there have been major disasters here in the US like Katrina.
As for Canadian pilots wishing to participate in PNP flights within Canada, I would ask an accountant if any of the expenses could be used as tax write-offs. I know all of us are doing this for the animals and not the tax write-offs but as someone else mentioned the write offs can help offset the costs of flying.
All of this being said, we will hopefully be making more frequent trips to Canada in the near future pending us getting our own airplane and if we have enough space would be totally willing to fly some pets!