Suppose that we want to compute a datagram hash, consisting of a $512-$bit header and a $512-$bit payload. We have a secure block cipher E with $512-$bit keys, $512-$bit inputs and $512-$bit outputs, and a secure internal hash function H with $512-$bit inputs and $256-$bit outputs.

Does Hash$($datagram$)=$ H$($Eheader$($payload$)$ XOR header$)$ provide collision security? That is enciphering the payload using header as the key, XOR$-$ing with the header, and then hashing?