Based on the classical earthly-branch relations of your two zodiac animals — this combination may emphasize these tendencies; real people add the nuance.
Punishment pairing — friction that sharpens
Monkey and Dog are in a punishment (Xing) relation — the classical name for two temperaments that rub each other the wrong way while chasing similar goals. The friction is real, but so is the sharpening: punishment pairs often achieve more together than either would alone, once rules of engagement are agreed.
Divide domains clearly (who leads where), and what was friction becomes productive tension.