You need an SDS drill and a suitable bit.
Rent or buy is the choice and you'll want to look at the costs. One hole, probably no more than an inch in diameter, through 24" of almost any rock should be no problem at all for any SDS drill, even a real cheapie. Look at the real cost of renting, including your time for collection and return and try to decide whether there is a real value to owning an SDS drill after the job is done.
Things to be aware of with SDS drills:
Speed is usually variable, but impact energy is not, at least to anything like the degree that speed is.
It's difficult to explain the difference between a hammer drill and an SDS drill to anyone who has not used an SDS before.
I once did a job where we needed to cut a 3" hole for a pipe through a precast reinforced concrete garage using a Carbide-tipped core drill, then drill holes for the pipe fixings. The core-drilled hole took 5 hours with a hammer drill, over an 8-hour working day, with 3 of us taking turns in between having to stop and let the drill cool down. The 6mm (1/4") holes for the fixings were taking close to ten minutes each until the drill threw a commutator bar. I went off to buy a new drill from the nearest DIY store and bought a small SDS, along with some bits. The next day, we drilled the fixing holes. My colleague timed me drilling them at 11 seconds each: a good 50 times faster than the hammer drill.
Back in the mists of time, drilling rock/brick/masonry/concrete/etc was done with a star drill: a chisel with a straight-fluted cross-shaped shaft. This was held in the left hand and struck with a hammer, rotated about 45 degrees and struck again. After doing this several hundred, or several thousand, times, stopping every now and again to clear out the debris, there would be a hole. It might be a 1/4" diameter and 1" deep for a plug (wood or fibre, not plastic: it was a long time ago) for a woodscrew, or 1" diameter and 15' deep for a blasting charge. It was a slow process.
When corded hammer drills became readily available, they turned pretty fast and hit very fast, but not very hard. They tend(ed) to be good for small holes for plugs and screws: certainly quicker and easier than most folk can do with a hammer and star drill.
SDS drills turn slower, hit slower, but hit a lot harder than hammer drills. It's the impact that makes them drill fast. Broadly speaking, the impact energy tends to increase with the weight of the machine and the rotation speed tends to reduce with the weight of the machine. The rotation speed isn't usually important to us, but the impact energy is. Here in Europe, weight is usually given in Kilograms and Impact Energy is usually given in Joules, with the impact energy broadly following a one Joule-per-Kg relationship. A 3 Kg-class machine would provide around 3J of impact energy and have a nominal capacity of around 26mm/1". The nominal capacity is just nominal, in the same way as a 1/2"/13mm rotary drill can usually drill a 5/8" hole without too much trouble, a 3 Kg-class SDS will usually drill a 30mm hole without much difficulty. 30mm diameter is the largest size drill bit readily available in SDS-plus. Above that, it's SDS Max and 5 Kg-class and upwards.
A bigger machine will usually drill faster, but for through holes, there is a risk that it will blow out the back of the wall when it gets close enough to the surface to knock out a conical lump. It's a risk with any machine, but a 2 Kg machine drilling a 10mm hole (3/8") in concrete might knock out a 1" cone, where a 10 KG machine might knock out an 8" cone. In brick, an overly powerful machine will tend to knock the back out of the brick being drilled, but the damage only usually goes as far a the mortar and doesn't affect the next brick. I had a 1.5 Kg machine many years ago, which let the magic smoke out and was replaced by a 3 kG machine. The bigger machine did enough damage to persuade me to buy a cordless SDS, which handles drilling through brick just fine (I live in Lancashire. The local brick is "Accrington Nori", which is about the hardest brick going. It was famously shipped over to the US to build the foundations of the Empire State Building because it is hard enough to support extremely heavy loads). Other bricks can be more, or less, prone to the problem and I'd expect a big variation in stone too.
In the OP's case, I'd recommend a maximum of a 3 Kg class machine (around 3J impact) and ideally I'd probably be looking for a 2 Kg-class machine (around 2J impact and probably rated to drill up to perhaps 22-24mm). The wall looks much too nice to risk making a mess of it, just to save a minute or two of drilling time. Any making good would certainly take a lot longer than the drilling time saved.
