We have our students target completing the courses/studies in about 3-4 weeks (studying ~2 hours a day). Even if it takes you longer or you're faster, this is a good target.
Once you feel like you're almost ready, you can start booking your exam with your provincial brokers association or regulator (ie. IBABC in BC, RIBO in Ontario, or AIC in Alberta). Information to help you with this step is included in the Introduction section of your course.
It should take about 1 week to get your exam time/location booked and confirmed but it varies depending on how busy they are.
After you have passed the exam and found an employer to sponsor your licensing application, they will help you complete the paperwork. Once you send it in to your provincial regulator, it should take 1-2 weeks to process but times vary depending on how busy they are.