Certainly, you'll need trailer brakes and one of the better trailer brake controllers. I'd suggest a proportional one. Maybe a Tekonsha Prodigy P2 or P3- but there are others. They're cheap and plug right in under the dash (order from etailer with the right cable). The plug is already there - even if you didn't get the factory tow package. You will need to have a proper 2" hitch with a 7pin connector, wired with 12V brake power and all. The harness is mostly all there right under the inside of the bumper.
I presume that the trailer that's 3700 is its GVWR not its dry weight. if so, you WILL be able to tow it, but you'll certainly feel like you're towing something huge. it will weigh about as much as the Evoque itself. Pay close attention to the tow hitch weight, as while the Evoque is spec'ed for a pretty substantial max towing capacity for its size of vehicle; it's max hitch weight is a bit on the low side (320lbs I think?). And, you'll exacerbate the issue if you also have stuff loaded in the back of your Evoque while you're towing. If you're talking about a travel trailer- they often give tow hitch weight without the weight of propane and batteries. Plus- how you distribute your belongings and water inside the trailer will also have a bit impact on hitch weight. You can help the problem with a weight distribution hitch... of course, they weigh something as well. But with a big trailer, having a weight distribution and sway control hitch will make everything feel way more stable and secure on the highway. I don't think it makes much difference for low speed towing.
Also the conditions in which you are going to tow will also make a difference. if it's just smooth roads, with no steep hills- then you can push the limits a bit more on the weight and 3700lbs will be good. You'll be impressed at what the Evoque can tug. I've found that off-road, and with short steeper inclines- things get a bit more dicey with a heavy trailer, and the weight of the trailer will yank the tow vehicle around quite a bit. I have avoided snow and ice with a trailer- so I don't have experience with that (I live in the southwest desert). Oh- plan on getting lousy mileage.

maybe 10mpg.
If you are looking at travel trailers- it really depends on your needs, but get as small and as light as you can live with. If the LittleGuy Mini Max S or
[email protected] 320 works for you- they'll be super easy to tow. A step up from there is something like a Forest River Rockwood Geo-Pro 14FK, maybe a Starcraft Autumn Ridge 14RB, or R-pod 171. Any bigger than that, and I'd only do it if you were towing on good roads. Many of the 16-17ft Travel Trailers come in sub 3,800, where you can have a walk around queen bed, a dry bath and even some additional bunk beds. Quite a nice setup for a couple or small family. If you are yanking it to campgrounds in Florida- you won't have a problem. if you are planning on boondocking in mountain wilderness areas... then it will be a struggle and you'll always be worried about your poor little evoque. But- from what I've seen so far..the evoque is a pretty tough little beast.
hope that helps.