  Using the technique of higher derived brackets developed by Voronov, we
construct a homotopy Loday algebra in the sense of Ammar and Poncin associated
to any symplectic $2$-manifold. The algebra we obtain has a particularly nice
structure, in that it accommodates the Dorfman bracket of a Courant algebroid
as the binary operation in the hierarchy of operations, and the defect in the
symmetry of each operation is measurable in a certain precise sense. We move to
call such an algebra a homotopy Dorfman algebra, or a $D_\infty$-algebra, which
leads to the construction of a homotopy Courant algebroid.
