Hi I have a 1960 Datsun Powered Morris Minor. It does have the Historic Rego here in QLD. Each state has different rules so you MUST check with the correct dept. in your state. Some states have concessional Rego, some have "permits". SOME STATES WILL OFFER REGO ON MODIFIED CARS AND SOME MUST BE ABSOLUTLY BOG STANDARD.
Here in QLD you can only drive the vehicle for testing purposes within 15klm radious of were you live, which means if you work 5 k's away from were you live you CANNOT drive your car to work regulary. You can take the car to and from a repairer with prior arrangements. And take your car on a gazetted club run anytime over any distance, or to club meetings. AND YOU SHOULD BE AN "ACTIVE" MEMBER OF A CAR CLUB AND THE CAR MUST BE AT LEAST 30 YEARS OLD. THE CAR CLUB WILL ISSUE YOU WITH A "DATING" LETTER FOR THE AGE OF YOUR CAR.
Car clubs are also bound to monitor member participation who have been accepted with Historic Rego. As this falls back on the club if a person joins and never goes on any runs or attends any meetings, this only leaves trips to repairers for the member to use his car. If member is caught it reflects badly on the Club and on the whole system.
There has been a fair bit of abuse of this system over the years and we get feed back from the Combined Council of Clubs that the registration dept is on the verge of scraping it as it is too much trouble to minitor. So a few bad eggs could be spoiling it for everybody else. this means everybody will be back to full rego and insurance costs.
SO PLEASE CONSIDER YOUR OBLIGATIONS BEFORE PROCEEDING.

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Just to clarify, do you have a Morris Minor that is powered by a 1960 Datsun engine, or do you have a 1960 Morris Minor that is Datsun powered? [wording is not clear]

I would have thought that an engine & gearbox change would be regarded as a significant & major modification, or variation from original, & thereby bar the car from Historic registration. Particularly if the engine is from an engine family that is still in current production. [South African Bakkie & also industrial engines]

The Morris Minor is a 1960 model
The Nissan Engine is about a 1970-80 vintage.

Whether is engine is still in production somewhere in the world I don't think is relevant, the point I was making is that here in QLD you can register such a car under the historical scheme, but in some other states the car cannot deviate from how it was originally produced, I have even heard of non-standard paint colours not being allowed, or radial tyres fitted.