It's great that you are planning a trip to Ireland and I'd love to help you further. 😊
A valid proof of vaccination or of recent recovery is indeed an exemption to the testing requirement. If you are fully vaccinated or recently recovered (in the last 6 months), you won't have to show evidence of a pre-departure test.
Please note that you will also have to fill out a Passenger Locator Form
I hope this helps.