The legislation mandating a 28 day waiting period states that the delay does not apply if you already have a weapon of that category under your license, I suggest sending an email to
weaponslicensing@police.qld.gov.au with a scanned copy of your PTA paperwork from the dealer.
Advise them that the 28 day wait does not apply to your current PTA as per Section 101 (3) of the Weapons Regulation 2016 and ask them to update your license details and waive it.
The previous PTA paperwork from the dealer could be lost or in a backlog pile that won't be processed for months or years, or ever.
They'll probably just ignore you and not respond but it's worth a try.