Get out the shovel
The Designated Hitter is supposed to be the best bat on the team, and it is supposed to be the best bat on the team who cannot play a position particularly well, whose defensive abilities would be a liability compared to another person on the team in the same position. In other words, Edwin Encarnacion. The Designated Hitter needs to be experienced, knows the game, knows situational hitting, and can threaten in clutch situations. None of these are Travis D'Arnaud.
There have been a few rookie DH hitters who went on to win Rookie of the Year honors. Evan Longoria was a DH in 2008, but he also plays third. Bob Hamelin is another rookie DH for Kansas City in 1994 but he also played 1st.
The position of catcher is highly specialized. Catchers are smart. They run the ball game defensively, calling the pitches, remembering who the hitters are. Athleticly, they need to be tough, crouching for all pitches, taking pitches, throwing quickly to bases, running down the line to cover plays, and being diplomats with umpires. There's a reason why catchers make great analysts in radio and television.
Putting Travis D'Arnuad, who has been called the best catching prospect in the game, at DH would be a waste of talent. He is unproven in the majors at the bat and will likely not be the best bat available at DH (Edwin). He is talented defensively at the position.
So, please Alex Anthopoulos and the Blue Jays, if you are going to consider putting Edwin on regularly at 1st and relegating Adam Lind to another team, please consider the free agent market and get a veteran in there instead of a DH. Travis D'Arnaud is a catcher, not a DH, and certainly not a rookie DH.
Don't kid yourself. Expect a trade of Travis D'Arnaud or JP Arencibia in the offseason, hopefully for a starter.