For 10 month old -
Nappies, wipes, teething toy, muslin, rattle / shaker, interactive (small) toy, picture book, sippy cup of water, rice cakes / snacks / puffs, emergency Ella's kitchen pouch, socks, change of clothes, sun cream, hat (either sun hat or winter hat depending on weather and if not already wearing), coat (in changeable weather if not already wearing), usually some homemade food (e.g. pesto pinwheels or savoury muffins or whatever).
For me -
phone, portable charger, umbrella, keys, wallet, makeup, kindle, socks (in case of impromptu soft play visit), spare contact lenses, sunglasses, noise cancelling headphones.