Is the change in enthalpy (ΔH) for dissolution of urea in water positive or negative?
The sign of Q depends on the perspective. The water temperature decreased because it "lost" heat. The process of dissolving urea required energy, it "gained" energy. If I give you a penny, should that be +1 or -1 penny? Well, it depends who you ask. 

In your answer, you are missing a negative sign in $\Delta H=−Q$ the way you start out with $Q$ from the perspective of the water.