To be a little bit more specific, as you have said, the common bird associated with Hecate is an owl, which represents wisdom and experience (the old lady), however you have seen white dove, which represents purity and new beginnings (Young girl, fertility). And instead of the crescent moon you had seen the eye (the full moon), the protective eye of the mother. It is actually interesting that instead of the protective aspect (hounds) you had seen the mother/child aspect of the lamb.