Exactly when the Irish stole the instrument from the Inuit (Eskimo) must have been at the time of Brendan's voyage to the New World.
Seriously, this type of percussion drum is widespread and it has a long history. How long have the Irish have had it ? No old data, a tall, a tall. It is related to the tambours of Africa and Asia, brought across the Behring Strait to the New World by the Inuit, but that doesn't answer the "Irish Question."
The suppositions by Malcolm Douglas are as good as any. The development from an instrument to separate grain from chaff is possible, and may explain the tambours, but the development from the minstrel show's tambourine seems more logical for the Irish version.