Ruaidhrí Dall Ó Catháin is supposed to have died around 1650. Before this date,
Irish and Scottish harps were all low-headed design. The most iconic example would be the medieval
Trinity College harp. These low-headed instruments have at least 29 strings,
and may have used precious metals in the bass to give a rich, sweet sound.
There is one extant harp that is securely dated to within the traditional lifetime of the Irish Rory Dall.
The Cloyne harp was made in the South of Ireland in 1621.
It is a characteristic large low-headed shape, quite large, and very solidly built and richly decorated.
The Cloyne harp is very unusual in being chromatic, and I imagine the Irish Rory Dall most likely had a diatonic
instrument. Perhaps his harp was something more similar to the Lamont harp, which bears an early 17th century repair and graffiti.
Ruaidhri Dall Mac Mhuirich was born around 1656. From the middle of the 17th century onwards, there were changes in musical instrument design and construction across Europe. It's not clear how long these changes took to reach Ireland and Scotland, and how long the older traditions continued.
There is one extant harp, securely dated to within the lifetime of the Scottish Rory Dall, which is characteristic of the new shape of early Gaelic harp. The Downhill harp was made in the North of Ireland in 1702. Its high-headed shape accomodates brass stringing from the top right down to the bass, and the long bass strings and longer, more slender soundbox produce a more growly, pungent sound. It has just 30 strings, which makes it a small harp by 18th century standards. The Scottish Rory Dall might have played a harp like this.
However older low-headed harps were still in use during his lifetime, and he may instead have played an older style harp like the Lamont or the Queen Mary harp, both of which were still being played elsewhere in Scotland until after his death in the early 18th century.