With an ILR, she should be able to travel to Ireland with the E.U. laws about travelling of family members of a E.U. citizen for stays under 3 months.
She should have with her her passport and documents stating her ILR. Having a copy of the marriage contract also if the passport is not amended under her married name may be useful in case.
If going by car and having no immigration control at the border may give a problem to attest the entry date in the country (for the 3 months limit). Better to use a road where there is a control.
To confirm, a phone call to an Irish consulate would be great (and a message here to let us know a must!).