In principle you should have access.
This is on the basis that you are holding a boarding pass in J for a Oneworld flight that departs within 24 hours. So if you present your onward DOH boarding pass to the lounge agent in DXB they might be momentarily puzzled but should work it out.
From
https://www.oneworld.com/airport-lounges
oneworld Lounge Access for First Class or Business Class Customers Connecting between oneworld marketed and operated flights:
- First and Business Class customers connecting on the same day of travel, or before 6am the following day, can access the lounge when travelling between an international long haul (a oneworld international long haul flight is defined as an international flight marketed and operated by any oneworld carrier with a scheduled flight time longer than 5 hours) and an international short haul or domestic flight (and vice-versa).
- Lounge access will be determined on the international long haul ticketed flight (either First of Business Class) regardless of the ticketed class of travel on the international short haul or domestic flight.
- You must be prepared to show your boarding pass or itinerary showing travel in First or Business class on the international long haul flight, in order to access the lounge before your international short haul or domestic flight.