家犬 is the formal/written word; in everyday speech people say
狗 (gǒu) or
家狗 (jiāgǒu). The
犬 (quǎn) form appears in scientific names, legal texts (
导盲犬 'guide dog,'
警犬 'police dog,'
军犬 'military dog'), and literary writing — same character, more elevated register.