I just brought 4 cats and a dog from Turkey to Canada.
2 of my cats flew with me in the cabin (aircanada allows 1 pet up to 10kg in the cabin for 1 ticket ) only paid 75 euros for each before taking off. The documents needed changes according to your country, for our case we needed to get clearence from Turkish Agricultural Dept. to be able to take the pets out of the country. The Canada part is easy, all they want is the rabies vaccination and they don't require a waiting time between vaccinating and the time of importation. They don't require a microchip or tattoo neither.. But I had my pets checked and had all the regular vaccinations just in case. The pet passport and the document from my country was enough to bring in my 2 cats. I didn't pay anything in Canada for them.
And for the rest of my pets I used AC Animals pet cargo. Because of the weather conditions (aircanada does not fly pets in cargo if the weather is above 35 degrees in either departure or the destination city) my pets had to arrive a week after me. The documentation was the same but it cost a lot. For my 35kg dog (plus 10kg for the case) I paid 1750 american dollars (ouch!) and at the customs in Canad while meeting them I had to pay approx. 70 cad (i can't remember exactly )
The cats in cargo was relatively cheaper, around 250 american dollars because the cargo estimates the fee according to kilograms or the dimensions of the case. They count whichever is the bigger. Cats' cases were smaller and they were also lighter so it didn't cost much.
So if your pet is below 10kgs, definitely fly with him in the cabin. It is not so comfortable but way cheaper.