Sorry I was thinking of dominion status as being more like devolution in Scotland then dominion status for Canada.
I think its GDP would be pretty close to what it currently is based on its population, and education system. It might get there differently though.
But a significant chunk of that is based off tax policies and incentives that even Scotland doesn't have the power to do right now, let alone through the the 20th century.
Instead I could see Ireland remaining a much more rural/agricultural nation for the most part with Ulster still having a heavier base, with the incentive still to go to the rest of the UK for higher end jobs. It's unlikely you'd see the Multinational invest to the size and scale of what we have now, or the support industries that sustain it. At the same time supporting a NHS system would be costly, would the UK invest in building up the infrastructure of Ireland?
There are plenty of butterflies but I think it's more than a bit off to suggest that automatically we'd end up with the same combined GDP (particularly as the Multinational's outsize Irish GDP, better to look at GNP)...