The Verdict: Need More Info
Your spouse must claim their Irish citizenship before this route opens for you. Ask them to apply for an Irish passport or a Foreign Births Register entry; your own clocks keep running meanwhile.
If your spouse was born on the island before 2005, or has a parent born there, they are a citizen or entitled to be one, and a passport application settles it; someone born in Northern Ireland becomes a citizen by claiming it. If the claim runs through a grandparent born on the island, they must enter the Foreign Births Register first, which the department estimates at around twelve months. A claim through a parent who was Irish but born abroad works only if that parent was already registered when your spouse was born.
Your clocks do not wait for their paperwork: three years of marriage, and three of the last five years living on the island with no more than 70 days away in the last twelve months. By the time their citizenship is in hand you may qualify straight away.
If your spouse needs to register and a child is due, a child born before the registration has no claim through them. An expected birth is a recognised reason to ask for the registration to be treated as urgent.