  We investigate a planar model for the ferromagnetic (FM) phase of manganites,
which develops orbital order of $e_g$ electrons with x$^2$-y$^2$-symmetry at
low temperature. The dynamic structure factor of orbital excitations and the
optical conductivity $\sigma(\omega)$ are studied with help of a
finite-temperature diagonalization method. Our calculations provide a
theoretical prediction for $\sigma(\omega)$ for the 2D FM state and are of
possible relevance for the recently found A-type phase of manganites at high
doping which consists of FM layers coupled antiferromagnetically. In the
x$^2$-y$^2$ ordered regime $\sigma(\omega)$ shows both a Drude peak and a
gapped incoherent absorption due to a gap in the orbital excitations.
