There wasn't an institution of knighthood in the sense of a title conferred upon someone with social benefits and the implication that one had a certain amount of wealth. Despite this, there were cliques of individuals who were called knights (curaidh) and functioned similarly insofar as they were aristocrats and warriors and prideful of that rank.

The oldest hint of anything of this sort is actually from Irish myth, where the demigod hero Cúchulaind is given miniature arms at the ripe old age of seven years! This sounds pretty fantastical, but Froissart describes this ritual surviving, at least for the sons of great lords, at least until his own time (ie post Norman).

These customs were so strong that when Richard II of England tried to ingratiate himself with the Irish kings by offering them knighthood, they kept refusing; their reply being, of course, that they had already received the honour at the age of seven. Nonetheless, Richard double-confirmed their chivalry through a second knighting ceremony.

The ceremony and dialogue between kings and king is related herein by Sir James Ware in the Antiquities and History of Ireland:

Froissart... tells of 4 Irish Kings... These Kings, after their Submission and Fealty acknowledg'd to King Richard, were committed to the care of... an English Man, who understanding the Irish Tongue, was commanded by the King to instruct them in the English customs, and particularly in that of receiving the order of Knightood...tho they alledged, that they had long before receiv'd it from their Fathers at the Age of 7 years, as was the custom among all the Irish Kings to confer it on their Sons. the Ceremony thereof was, that at the time of the creation, the youths armed with slender Speaers, proportionable to their strengths, run some courses against a shield set up in the Midst of a Field, and he that broke most of those spears, had the greatest honour.