It is inappropriate IMO.
Couple of reasons: as intimated, short trips/low mileage isn't good for a diesel engine. Something about a particulate filter clogging up? I'm not exactly sure. You may not have any trouble at all, but diesels are designed with longer journeys & mileage in mind - that's the point of them.
The other thing is, at only 3K a year, it is unlikely that the added cost of buying a diesel would outweigh the fuel saving benefit - you could get a petrol equivalent of your vehicle for less money, with less mileage in the first place and have less of a concern about the short low mileage trips too.
When you say automatic do you mean diesel auto or petrol auto?
Edit: just noticed your other thread. Don't know much about diesels myself but yes, this filter clogging thing seems to be a common enough story.