Malé zvíře is the main translation but zvířátko is what any Czech would actually use. Czech has a passion with diminutives. Instead of saying "small this or that", we use a single word in diminutive form to describe it.
Dítě = děťátko Holka = holčička Chlapec = chlapeček Pes = pejsek Kočka = kočička Dům = domeček Auto = autíčko
and I can go forever.
Small Czech kids usually use diminutives before they even use their "regular" counterparts.