These questions are retarded as hell. It's been only 4 weeks into the season. Do the math. Add 8 weeks.
Each season is roughly 10 weeks. Then there is always 1 - 4 weeks of down time.
The PTR IS FAR FROM BALANCE. All these buffs were needed when firebird archon reign supreme from season 5 - 8. Season 9 - 10 was MH ARCHON. For 6 seasons the barb was underwhelming. They need to buff all the classes but the necromancer now because of the major power creep. Based on all these set buffs LoN is becoming useless now.
They might as well give all mobs the juggernaut affix just to balance this power creep you keep begging for.
MaraxuS80's estimate seems pretty spot on. Also keep in mind that they might adjust season length depending on if they want it closer to Blizzcon - or rather have S13 stuff ready on PTR for after Blizzcon, so this season can be potentially longer or shorter as usual. But I cannot imagine anything before end of September as Don Vu said in a bluepost they have a new balance patch for PTR that'll be deployed on September 10 or so, therefore I think a slightly longer S11 and a S12 that is still "fresh" during Blizzcon isn't entirely unlikely either.