If you want to immigrate to Quebec, you have to pass the Quebec selection criteria before going to the next step and applying to CIC.
One of the differences between immigrating to Quebec and immigrating to another part of Canada is that, in the case of Quebec, you must normally "land" in Quebec. If you "land" in another province you may be expected to show proof of immediate onward travel to Quebec. (Unless you are part of a specific province's [Provincial Nominee Program], it normally is not necessary to "land" in the province in which you intend to settle.)
The process of immigrating to Quebec is explained very clearly and thoroughly in the Immigration and settlement in Quebec section of the Quebec government's website.
When approved by Quebec you receive a "Certificat de Selection du Quebec" (CSQ). Then you can apply to CIC who undertake medical and security clearances.
As part of the CIC application process, a Quebec applicant will be asked to sign a declaration of intent to reside in Quebec. It is possible to move provinces later on, but only safe to do so after making a genuine attempt to settle in Quebec.
It is possible in practice (but not in theory) for a federally selected immigrant to move to Quebec. If you indicate on your federal immigration application form that you intend to settle in Quebec, you will be referred to the Quebec government. Also, if you try to "land" at a Quebec port of entry without a CSQ, you may encounter problems unless you can show immediate travel to somewhere outside Quebec.
Once you have "landed" somewhere else in Canada, you can then move to Quebec if you wish. However, if you can speak French it would usually make more sense to apply to Quebec initially if that is the intention. Also, permanent residents without CSQ do not obtain French language tuition, access to immigrant settlement services, and may pay higher university fees than those reserved for Quebec residents.
If planning to immigrate to Quebec, you should be aware that under Quebec law, immigrant children cannot be enrolled in the public English language schooling system. They must either go to a public French language school, or go to a non-government private school (expensive). The exception is normally if one parent is a Canadian citizen educated in English in Canada.
These restrictions on schooling apply until Secondary education finishes (17). Children of parents on work permits are not subject to the restrictions, and it is a consideration if on a temporary permit in Quebec and contemplating whether or not to become a permanent resident.