My whole dash board is missing!

laws vary state to state, but first off, I would recommend the local post of the state police or state highway patrol. Each has inspection program and methods for straightening this kind of thing out. (Salvage/Crash repair, etc).
Common sense states however, that if you have the title to both vehicles, then you will be fine. A huge majority of our friends in blue will look at the dash and nothing else, they may not know that anything else even exists. If push comes to shove, you show the data tag, the matching body numbers and the title to the dash you lost.
Proof of ownership of both pieces will keep you out of trouble.

Being an official member for only a couple of days myself, still have to say welcome aboard. I find the site incredibly useful myself and i'm sure you will also.