How do I travel around with a large dog in Spain?

Hello there We are settled near Murcia and plan to travel by ferry to Mallorca to visit my sister for Christmas - with the dog. She's a 23 kilo lurcher (so not a dangerous breed) - in fact a VERY friendly, lovely dog. But how on earth (without a car - ergo on public transport) are we expected to travel from Murcia to Denia Port to get the ferry with the dog? It seems that unless you have a small rodent or diddy dog, you're not welcome on any public transport. Is this true? Any ideas welcome Thanks