Routes For Primary TeachingWatch
QTS (Qualified teacher status) is a separate thing where you have to meet the Teachers' Standards Your provider does not award this but can recommend you for it. For most people they will be able to show that they are meeting these standards after ~120 days in a school. So you will normally be assessed near the end of the course you are on.
So if you were doing a PGCE Primary both the PGCE and QTS would be conferred to you at the end of the course. It is possible however to get your PGCE and not meet the Teachers' Standards by the end of the course (say you missed a lot of placements time due to illness). In which case you may need to extend your placement at school to meet the Standards which could drag into the next academic year. In theory the opposite could also happen (gain QTS but not meet the standards for the PGCE) but I've never known that to happen due to how the courses are structured.
TL/DR - For the majority of people they get them both at the same time.