I’m Czech and it’s “ta kočka ♀/ten pes ♂” too. The terms “kocour” and “fena” also exist but exclusively mean tomcat and bitch, never the species. In rare cases, the species name, the male animal and female animal are all different, but the species is still gendered because of grammar:

🐎 kůň (♂): hřebec ♂, klisna ♀
🐓 kur (♂): kohout ♂, slepice ♀
🐝 včela (♀): trubec ♂, dělnice ♀
🐖 prase (🇳): vepř ♂, bachyně ♀

Baby animals use the neutrum genus: _🐈 kotě, _🐕 štěně, _🐎 hříbě, _🐤 kuře, _🐖 sele