"She has a peach."
Translation:Tá péitseog aici.
Sorry, but that's utter nonsense.
Tá péitseog aici does not mean "There is a peach at her", it means "she has a peach".
If you insist on trying to interpret it as though it was an English sentence instead of an Irish sentence, then "a peach is at her" is no more nonsensical than your "there is a peach at her".