Welcome to Physics StackExchange!
If both you and the sledge are on a frictionless surface, and the rope is massless, then yes, your application of Newton's third law is correct, you will accelerate towards the sledge at 1.6 $m/s^2$.
If you are on rough ground (but the sledge is on a frictionless surface), then the ground exerts the same magnitude of force but at an opposite direction to the tension, such that the net force on you is zero; then you won't move.