Sounds good, but the big question is, where is Ireland supposed to get the money to pay for your AU Navy. Just as a real life point. New Zealand gifted the BC New Zealand to UK and had to take out loans to pay for it. Despite the ship being scrapped due to Washington Treaty, NZ did not actually clear the last loan payment till 1944-45.
Ireland has no bigger economy than NZ, and most of the money made in Ireland goes across to England as a lot of the land is 'owned' by the absentee Lords during the time period you are using 1845+. Since 1800-01 Ireland has been part of the Great Britain and Ireland Union. Ireland being no better off than Scotland or Wales. Ireland would not have any separate armed forces till Ireland becomes independent.
Harland and Wolf of course is funded by Great Britain, all the coal, iron etc to make HW run is also imported. If Ireland becomes independent too early, before HW is formed, then Ireland would have to find the funds to create its own industry.
Some fair points but bare in mind the suggestion that the Famine is going to be reduced/not happen, if that's so, ireland would have a population twice as large as NZ has now. Yes the majority was poor but if you do have an Irish Parliament then that might be different by post 1900. Maybe earlier land reform schemes then otl for example.
In terms of the navy Cobh would have to be built up during this period (and much larger than otl), pre 1800 (I think have to check) Kinsale was the main southern RN base, so Ireland would have to fund the fortifications of Cobh and the base as well.