Zoe, I think the form of both of these questions is correct, but they would be used in different ways and to exact different information from the person to whom they are being posed - although with No. 1 written in the passive tense it could be seen as being more formal than No. 2 (in perfect tense).
With No. 2, the questioner wants to check that the invoice has already been written/sent; in No. 1, the question is more about whether or not the invoice is in the process of being written/sent.