Looks like a sensible trailer for the money.
Maybe wait and see what tyres they actually deliver? Knobby tyres look like they might spray up too much dirt and water from the road, and be a bit muckier to store (I'm thinking: easy enough to avoid doggie doo-doos on a bike, less so with two extra wheels...).
The Carry Freedom came with Big Apple copies from a Taiwanese firm, Gumonder. 16" x 2" (ETRTO 305-50) - fat and smooth seems to make sense for trailer tyres.
Not an expensive fix to fit other tyres though, and they ought to last for years. Get ones with a reflex stripe for safety while you're at it.