.. to the Republic of Ireland

I believe the above in Irish would be

Tá uaim Poblacht na hÉireann a dul

Thoughts?

It would be:
Tá uaim dul go hÉirinn / go Poblacht na hÉireann.

The word-order OBJECT + a + VERBAL NOUN is used with direct objects (to eat an apple, to read a book), not with anything that starts with a preposition, or with adverbs.

Tá uaim úll a ithe (to eat an apple)
Tá uaim leabhar a léamh (to read a book)
Tá uaim carr a thiomáint (to drive a carr)...

but

Tá uaim fanacht anseo (to stay here)
Tá uaim éisteacht leis an fhear sin (to listen to that man)
Tá uaim amharc ar an teilifís (to watch tv, in Irish "to watch ON the tv")

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Oh.... never quite got that from the Duolingo course. That explains a lot. Thanks much.

You can also just say "Ba mhaith liom dul go..." "I would like to go to..."

Redwolf

... and the go doesn't appear in the question form:

Cá bhfuil tú ag gabháil/ag dul? Where are you going? (also Cá bhfuil do dhul?)


With some verbs there is a difference between the presence and absence of go:

Shiúil sé go Dún na nGall. "He walked/travelled to Donegal."
Shiúil sé Dún na nGall. "He walked/travelled through(out)/all over Donegal."

Shiúil sé an bóthar. "He walked along the road."
Shiúil sé go dtí an bóthar. "He walked to the road."

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WARNING: Intermediate speaker - await further opinions, corrections and adjustments before acting on my advice.
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), agus Gaeilge an Chaighdeáin Oifigiúil (CO).