Congratulations and have a safe trip home !
If the car has a 1275 and drum brakes, then the engine is a transplant. The 1275 engine could be from several sources. It could be a Cooper-S, it could be from an Austin-America, or it could be a much later A+ 1275 engine. Start by looking at the gearbox by crawling under the car.
If you find a LONG aluminum housing going from the back of the gearbox to under the shift lever, that is a remote shift. There are two types. One has (4) vertical bolts connecting the long aluminum housing to the bottom of the gearbox. That's a Cooper/Cooper-S remote. If you find there is a plate sandwiched between the aluminum housing and the gearbox and that there are horizontal bolts connecting that plate to the gearbox and housing, that is an Austin-America remote shift. If instead you find a whole bunch of rods running from the back of the gearbox to just under the shift lever, that's a later rod-change gearbox. While you can mix and match gearboxes and engines with some success, it is very likely that whoever put the 1275 in this car used the gearbox from the same donor vehicle so the gearbox may help point to where the engine came from. There is also the slim chance that whoever transplanted the engine used a "pudding stirrer" (a.k.a. magic wand) gearbox but it is very, very uncommon for someone transplanting a 1275 to do that. Let us know what you find.
Also look at the engine itself. If it has a generator as opposed to an alternator, it is not likely to be an A+ engine. However, alternator upgrades are common so finding an alternator does not mean this is a later engine. Other outward engine differences are going to be subtle. On the back of the block (where you cannot easily see) there will be removable tappet cover plates for Cooper-S 1275 engines. The Austin-America engine won't have those. A Cooper-S engine will have come from the factory with (11) studs/bolts to hold the cylinder head down. However, it was not uncommon to modify heads and blocks for other 1275 engines to add the extra (2) fasteners (standard engines having (9) fasteners from new). The front plate on an Austin-America is larger and has ears for engine mounts. If you look at the engine below the alternator/generator and see excess sheet metal pointing towards the grille (or evidence that something has been "hacked off" there) then you are likely to have an Austin-America 1275.
It is common practice to upgrade drums to disks when 1275 engines are fitted. The argument goes that if you have more power you are going to use it so you need to be able to stop better. The argument going the other way is that if you drove your 850 or 998 Mini like a normal person and do not drive any differently with the 1275, you don't need bigger/better brakes. After all, you are not driving with your feet on the brakes and gas at the same time and you have not changed the mass of the car. Regardless, it's generally considered a safety improvement to put disks on when a 1275 is fitted. Be advised that if your car still runs 10" rims you want the 7.5" Cooper-S brakes, not the 8.4" disks which were used on later Minis. The 8.4" disks will not work with the 10" rims without major modifications. There are other brake swaps available but they have their drawbacks. After you have driven your car for a while and know you want to keep it you can look into a brake upgrade. Though complete upgrade kits are available, most people buy a set of used parts and recondition them for about 1/2 the price.