Pets can be brought into the country if accompanied by an International Certificate of vaccination and veterinary examination.
The most recent date of vaccination must not be more than a year from the date of entry into Croatia.
The veterinary examination can be effected at the border crossing (in which case a fee needs to be paid). Pets are not subject to compulsory quarantine, but they must be properly vaccinated (against rabies) and have confirmation on that.
For up to date official information, contact the Ministry of Agriculture: http://www.mps.hr/default.aspx?id=6260.