As with Airbnb everywhere, whether a Spanish listing welcomes pets is the individual host's decision, stated in the listing's House Rules section. Hosts in the countryside and in cities with a strong café and terrace culture often welcome pets, but it's never guaranteed by default, and shared apartment buildings or listings with delicate furnishings sometimes specifically exclude them.
If the listing is silent on pets either way, message the host before booking rather than assuming. Spanish hosts can decline or cancel a booking if an undisclosed pet turns up, and Airbnb's standard cancellation terms rarely favour the guest in that situation.
Ask specifically about any pet cleaning fee, whether the property has a secure outdoor space, and how close it is to a park or dog-friendly walking route — and if your dog could fall under the PPP system, mention that directly, since some hosts set their own breed restrictions on top of Spain's national licensing rules.