Hi Taffy
Quebec immigration is basically an extra step to the Canadian immigration (CIC)process. Whether you file in-land or out-land, once CIC has given you Approval in Principle (AIP) they will forward your application to Quebec Immigration (MICC). MICC then mails you the forms to complete, you fill them in and send them back with your payment. Once MICC approves you they will forward your application to the appropriate visa office for processing.
You can see and download some of the forms from the MICC website
http://www.immigration-quebec.gouv.qc.ca/en/immigrate-settle/sponsors-sponsored/requirements-sponsor/index.html but
please note, there are further forms to complete that will only be sent to you from MICC itself once they get your application from CIC. At the moment it seems MICC are taking 11 weeks or so to get those forms out but I haven't seen any information on how long they take to process them once received. Someone might read this and have some information they can share!
From other people's comments it seems the MICC approval is mostly a formality (since CIC has already approved you), at least I haven't seen a posting of someone being accepted by CIC but not by MICC.
Hope that helps.