You do indeed as enshrined in the the [broken link removed] and lack of a warranty registration card doesn't effect them one whit.
Where goods are defective or break down after a sort period (IMO 2.5 years for a stove is a short period) your recourse is against the person who sold you the stove, the hardware shop or installer and not necessarily the manufacturer, unless they sold directly to you.
If you register for a manufacturer's warranty, this warranty operate in addition to your legal consumer rights; not rgfistering your warranty in no way diminishes your legal rights as a consumer in Ireland.
You will need :
a) proof of purchase, a receipt is good, but a bank statement, cheque-stub or credit card slip or statement is just as good
b) some independent verification that the stove is in fact broken and not just cosmetically damaged.
See here for more info - [broken link removed]
The issue revolves around "how long would a reasonable person expect a properly used and maintained solid-fuel stove to last?"