Kristine,
IELTS isn't required to apply for CSQ. That's only to get extra points if you need some to meet the minimum threshold. Also, unlike for FSW, IELTS value is miserable in terms of points awarded even for an advanced proficiency. You can send your application if you have the minimum points and then update your file with IELTS result. You'll need to start learning french. That will be one of the most important aspects of application. The processing time will mostly depend on if your profession is in the priority list. Calculate your overall points via this link http://www.canadavisa.com/quebec-skilled-worker-immigration.html