It isn't that simple to mix the series. HP has its magic where the characters are innately magical and with a wand to focus that they can cast spells. In GD mages access the ether stream to cast spells (different types of mages do it in different ways, for example: war mages focus the ether through their own bodies.)
You forget the most distinctive part of GD's magic also. It can't be used against metal. Also, it can't change things on an atomic level. Harry Potter magic could likely be very powerful against GD simply because it doesn't have those glaring weaknesses. Any fic would have to explain why HP type magic doesn't have these weaknesses.
You also have the differences in both series ways of keeping secrecy. HP has been obliviating muggles since the 1700's to keep themselves unknown. GD on the other hand, had their magical races move to Jade millenia in the past. You'd have to combine the two and find an explanation for why the HP wizards didn't go as well.
While these series can be crossed, it would take more explaining than I'd care to do.