the parrots food should be fine, just read the ingredient list (it should have a list) and run it against the list of foods dogs shouldnt have. (pistacio nuts are one that comes to mind)
we have a goffins cockatoo who sometimes throws his food (and my mum occasionally drops some during feeding time) and the chis love to snack on it lol.
they've eaten sunflower seeds, papaya, peanuts, cashews, weaning pellets lol...so far no problems and the vet said the only thing we need ot be carefull about would be the peppers (the seeds getting in their eyes) and the choking hazard...
other than that the actual food itself shouldnt do them any harm.
and welcome aboard Ruby