Do what makes YOU feel safe and be safe! And yes, abide by your local laws first (I can't believe I just said that

....).
I don't know if I would use a WDH on 3000lbs, but you're also going to be loading it up, I assume the GVWR of that trailer is 5000lbs, given the dual axles? It also depends on your tongue weight, a 3000lb trailer could have 450lbs (15%) of tongue weight really quickly, if not more once loaded for a trip, and start to make the steering light. Then you might want to think about a WDH. I use a WDH (3800lb Dry, 6000lb GVWR, 25ft OAL) and depending on how the vehicle felt with 3000lbs, I may use one for that as well.
(I think a lot of people would be surprised if they weighed the tongues of their "light" trailers before a trip.

)
If you decide to go with a brake controller. My rule of thumb, if the trailer has electric brakes, regardless of weight, get a controller (seems like obvious advise!

). I would recommend electric brakes on anything over 2500lbs just because it's less strain on your tow vehicle braking system.
I have the Red Arc Tow Pro Elite in my Touareg more recently and in my Tacoma for several years now. It's maybe $30-50 more expensive than some other brands, but it's such a smaller "footprint" in the vehicle. There is a good write up on this forum somewhere as well as on etrailer in regards to locating and wiring the plug assembly mentioned earlier.