I don't know about an Inkdawn, but I do know about an Inkdeath. Inkdeath is the last book in the Inkheart trilogy. Book 1 is Inkheart, book 2 is Inkspell, book 3 is of coarse Inkdeath. Further notice on whether Cornelia Funke is writing another book I am not aware of, but who knows.
The first book is called Inkheart, then comes Inkspell, then comes Inkdeath and I think Cornelia is now writing Inkdawn. But you could get a second opinion if you like.
The title of Cornelia Funkes third book is Inkdeath.
i dont exactly know if they'll stay together at the end but i do know that there will be another boy