In theory, you can tour on any bike. In reality, you will be much better off with a bike optimized for touring.
Compared to a racing bike, a touring bike will have a longer wheelbase, lower gearing (road bikes have a low end around 34", touring 27" or lower), wider tires, a more relaxed geometry, lots of braze-ons. Bike / frame weight is unimportant with a touring bike, whereas "light as possible" is a selling point for racing bikes. You will likely want a moderately upright riding position for touring, whereas the tendency with a racing bike is for a flatter / lower posture.
You may also want some suspension on the touring bike. Fortunately, that's an easy item to add to almost any bike, with a suspension seatpost like a Thudbuster.
Another thing to keep in mind with a trailer is that since it's rather capacious, you will be tempted to bring a lot of stuff with you. This may be good (you'll have creature comforts) but it may also be a drag (more stuff + trailer itself = more weight than panniers).