Bonus info: A Danish fuel company ran a campaign in the 00's using the words "Vildt dyr" ("wild animal"/"wildly expensive") to a background of tigers and then cutting to "Vildt billig" ("wildly cheap") with one of their gas stations in the background. They did the same with "Enormt dyr" and an elephant.
Well, you could say the same thing as a word play but it sounds a little far-fetched (just like the English sentence does). In such an event, I guess we would say "Transporten er med dyr", but it would be still more likely that we'd say "Vi kommer derhen ved hjælp af dyr" or "Vi bruger dyr til transporten". Some might say it's a bit weird to travel by unspecified animal, but maybe the species is a surprise...
No. It wouldn't be quite the same. "The transportation is expensive" is the literal translation of the sentence above. It sounds fine in Danish. In English, you'd probably say something like "Transport costs are high" or "There's a considerable transportation expense". Or you'd use "travel". But "travel" means humans are moving. "Transportation" can just as well be objects. So the words have different meanings.