You cannot catch ghosts in The Sims 3: Pets. Ghost hunting is exclusive to The Sims 3: Supernatural (Expansion Pack 7, 2012). Pets (EP5, 2011) adds horses, cats, dogs, and unicorns—no occult mechanics.
Solution: Buy The Sims 3: Supernatural (often $5–$10 on Origin/Steam/Keyshops). Install via EA App. Load save → Ghosts now exist.