Really? I don't understand that. The power isn't in dissolving the Dáil itself, it's in the choice to do if it's deemed appropriate, whether the Taoiseach wants it or not.
When the Queen dissolves parliament she's just going through the motions, it's a formality. If she had refused, say, Theresa May's request for a general election in 2017, saying that there was no need as the Government had a clear majority and Brexit needed to be the focus (and she did this by either hiding down the countryside, not answering her phone or by shooting down the idea preemptively) that would be a huge deal. That would be her exercising her power.
When the Queen dissolves parliament she's just going through the motions, it's a formality. If she had refused, say, Theresa May's request for a general election in 2017, saying that there was no need as the Government had a clear majority and Brexit needed to be the focus (and she did this by either hiding down the countryside, not answering her phone or by shooting down the idea preemptively) that would be a huge deal. That would be her exercising her power.