Too many people wrongly believe the person listed on the registration document is the legal owner. That's not the case. It's especially apparent if the 'owner' has money still outstanding on the vehicle (to a bank or lease company). In such cases, such interest would almost certainly be registered on the PPSR.
The registration authorities only cares about noting the registered operator and getting their yearly fee. They want the registered operator details so they know who drives the car and thus who to send any speeding fines to
They do have an interest in knowing when the registered operator changes hands since they want to get paid any stamp duties owing (and still need to know who to send those pesky speeding tickets to).
(Oddly, companies are also considered 'people' from a legal perspective. So companies can be listed as the registered operator of motor vehicles. Some use this oddity to get away with having their business pay a bigger fine sans loss of a drivers demerit points)
Neither the rego authorities or PPSR guarantee who the legal owner actually is. Legal ownership is a contractual issue that the rego authorities don't car to be involved with, other than to get a few dollars of stamp duty out of any transaction
In your case, if the car was registered in QLD at the time of sale, then the QLD authority should have been notified of either a change of ownership usually within a 14 days of sale (and any taxes owing paid) or the registration should have been cancelled at the time of sale (then it's none of their business.
If the car was registered in QLD at the time of sale, and you bought a PPSR certificate showing no encumbrance (no other party had any interest in the car), that certificate along with a contract of sale and proof that full payment was made is all the proof anyone needs that the car is yours. Generally the sales contract and payment receipt is enough to prove ownership. Obviously it's always better is you had such docs tracing back the history to the original purchase from some dealer, ideally to the original dealer (provenance).
But from your perspective, being a modified vehicle, what would have been much better was to have all the engineering reports/approvals, receipts for parts (with VIN number of donor vehicles if used parts), receipts of work done (by businesses) any other relevant docs provided to and associated with the QLD registration modification plate. That way you can actually check that the mods on the car line up with the mods approved/accepted by the engineer/registration authority. Such docs may have made it a little easier to register the vehicle in NT... Such documents have a lot of value...
So, the problem you may now have is not so much about "ownership" but more about proving the engineering work that was done. Without such docs, it makes the vehicle much less valuable to someone who needs such engineering docs (so they can register it in their state)... Even if someone from QLD buys it, without such docs, re registering it may be a problem (dispite the mod plate and the rego authority having documentation on hand for the mods they approved).
Getting stuff re-engineered post modification may not be so simple. In
@Ron Burgundy case, he needed specific info on the receipts for his Brembo brake mod, Ebay purchased calipers were not considered acceptable. Easy to do before the fact but imagine turning up to an engineer asking for certification after buying some Brembo Ebay specials and fitting them to your car... you may have all sorts of difficulties... the more mods, the more difficulties...
As for the procedure for selling, sign contracts and get fully paid before the owner arranges pickup or delivery
