Do I need a passport to be valid for a certain period?

This depends on where you are travelling to. 

European Union

Your Irish Passport must be valid up to your return date.

United States

Your Irish Passport must be valid up to your return date. And you must also get an Electronic System for Travel Authorisation (ESTA) under the Visa Waiver Programme for entry into the United States. You can find more information on the US Embassy in Ireland's website.

All other countries

The passport validity required for countries outside of the European Union and the United States varies greatly so contact your travel agent or the embassy of the country you're travelling to for the most up-to-date requirements. 

For China you will need at least six months left on your passport. Before applying for a Chinese visa you should check with the Chinese Embassy you are applying to, to confirm their requirements.