Count: 0 — No European countries start with Q. For an A–Z reference of European countries, capitals, populations and official languages, authoritative sources such as the United Nations list of member states, Eurostat and the CIA World Factbook show no sovereign state in Europe whose common English short name begins with the letter Q. Note an interesting detail: only one UN member state worldwide begins with Q — Qatar — and it lies in Asia, not Europe.
Explain why the search yields no results. Remember that English short names for European states derive from local and historical forms that seldom begin with Q, and transliteration rules usually render similar sounds with K or C (for example, Kazakhstan appears in some Latin-script Kazakh proposals as “Qazaqstan,” but the recognized English name is Kazakhstan). Flag Q-like near-misses: Qaraqalpakstan is an autonomous republic within Uzbekistan, not a sovereign European country, and dependent territories or regions (for example, named places that start with “Queen” or “Queenstown”) do not qualify. Consult the UN member-state list, Eurostat country lists, and the CIA World Factbook when compiling an accurate A–Z reference, and focus on letters that actually produce entries for Europe.