Those should be the right names, but I may have missed a few fada in the spellings. In any event, Domnall wasn't king (wasn't even claiming to be in 1080, yet, and Toirdelbach was pretty solidly king of a bit more than half of Ireland). It's notable that when Toirdelbach died, even his northern rivals recorded him as 'King of all Ireland', which they rarely applied to high kings from the south (Leath Moga), choosing typically only to recognize kings from the north (Leath Cuinn) as true high kings due to Niall of the Nine Hostages and his progeny (the Ui Neill tribe and the associated clans). However, Toirdelbach's authority, and his seizing of Teamhair (Tara), coupled with his powerful army and a pretty loyal host of underlings (though his authority in Leinster was maintained in part by playing the rival Ui Dunlainge and Ui Cheinnselaig against one another to keep them too busy to be any bother to him) made sure he got recognized as king.
Domnall's name is funny. Only sometimes is he called Mac Lochlainn, which, by Irish patronymics, is incorrect. His obituary uses Domnall mac Artgair meic Lochlainn, but he was most often called Domnall ua Lochlainn (Lochlainn being his grandfather).
The Irish dressed the same as Scots, but without Scots in the old style clothing, I don't know what you'd really want to do with their clothing, lest some one can make the leine and bratt. Professional Irish soldiers certainly shouldn't wear trousers though, it's below their station. The large padded coat would be pretty accurate armor for most mid-class Gaelic soldiers, though it'd have been worn with a cloak. The best advice for their equipment I can give though is to make sure they have loads of javelins.
Edit:
Picture added. Actually medieval Scottish highlanders and islanders, but the Irish dressed the same as this, except they'd have cloaks.
Also, the main associated colors the Irish used at the time were blue, yellow, and red. Green was most notable on the banner of the kings of Leinster. The high king's banner was probably that of the Munstermen at the time, which was probably NOT the modern flag of Munster, that is, the three gold crowns on a blue field, but it was probably blue, due to the myth of Mor Muman, a woman who represented the land and was 'married' to the lawful kings of Munster, who wore a deep blue dress. However, it may have been the flag of Mide, depicting the high king seated on a throne, on a soft blue field.
Edit 2:
Also, on the Irish (and Scots, for that matter), stat-wise, they should be very fast moving, relatively. Among the key attributes of Gaelic warriors was their ability to fight effectively even in poor terrain by superior use of their mobility. The Irish, during the Cambro-Norman Invasion, did best by luring Norman forces into wooded or marshy areas, then flanking them at the same time as a frontal charge. Their superior speed and mastery of the shieldwall allowed them to rip apart medieval Norman-English forces in such conditions with minimal casualties. It should definitely, I think, be one of their big strengths, coupled with the prevalence of javelins to weaken and disrupt the enemy line during the charge. Also, on the march, the Gaels could cover huge amounts of terrain swiftly. The only English comparison I can think of is Harold's hasty move south to engage the Normans, and Saxons had a similar infantry focus (though not identical).
OH! And some fun characters maybe, Ulf and Harold. They'd be 14 in 1080, but were the sons of Harold Godwineson, and were probably in the court of Leinster. Harold had been a friend of the Leinstermen, and allies. Leinstermen and Dubliners had even tried to help invade England to restore the Saxon kingship. The twins, or their cousins who were also in Leinster, could be some great characters. Like, having a quest for Irish characters to raid Cornwall in exchange for a Saxon hero joining them, with his personal guards (good quality Saxon warriors), and maybe more if there are successful raids in England. I don't know how well that'll work, but, it's a thought, and would exercise the political dynamics of the day between the islands.