We determine the excitation spectrum of a bosonic dipolar quantum gas in a one-dimensional geometry from the dynamical density-density correlation functions simulated by means of reptation quantum Monte Carlo techniques. The excitation energy is always vanishing at the first vector of the reciprocal lattice in the whole crossover from the liquidlike at low density to the quasiordered state at high density, demonstrating the absence of a roton minimum and thus the absence of superfluidity in the Landau sense. Gaps at higher reciprocal-lattice vectors are seen to progressively close with increasing density, while the quantum state evolves into a quasiperiodic structure. The simulational data together with the uncertainty-principle inequality also provide a rigorous proof of the absence of long-range order in such a superstrongly correlated system. Our conclusions confirm that the dipolar gas is in a Luttinger-liquid state and that the Feynman spectrum inferred from the static structure factor yields in most cases an inaccurate description. The connection with ongoing experiments is also discussed.