Your pet can travel on the plane with you (either in-cabin, as accompanied baggage, or as cargo). Your pet will be charged accordingly. Some airlines no longer offer this option and some countries do not allow pets to enter the country in-cabin. You can book your pet on a separate flight.
Does Aer Lingus allow pets in cabin?
Aer Lingus does not accept pets in the cabin of the aircraft with the exception of trained and certified assistance dogs. Assistance dogs flying within the EU must be trained by an organization associated with Assistance Dogs International or International Guide Dog Federation serving disabled passengers.