You are still at the very initial stages. Sponsor elligibility is to determine whether you meet the requirements to be a sponsor. That is the first step after AOR. Sponsorship in general take around a year but can be shorter or much longer.
My PR tracker shows everything completed and I received pre arrival letter. But for my dependant son it shows eligibility and background not yet started. What does it me, is my son's application processed separately, he is 17