We provide a field-theoretical description of thermal nucleation in a one-dimensional ferromagnetic superfluid, a quantum-gas analogue of false-vacuum decay. The rate at which ground-state domains nucleate from fluctuations in the metastable phase follows an Arrhenius law, with an exponential factor determined by a saddle-point configuration of the energy functional – the critical droplet – and a magnitude fixed by small fluctuations of this configuration. We evaluate both contributions over the full parameter space, using a Gelfand-Yaglom approach to reduce the calculation of the fluctuation spectrum to an initial value problem. In addition, we obtain a closed-form expression for the critical droplet in the limit of small potential tilts, and use it to formulate an effective theory of domain nucleation and growth as a Kramers escape problem for the droplet size. Our results determine the parametric dependence of the nucleation rate and its signature on experimental images of a nucleating gas, and should allow for a rigorous comparison between nucleation theory and experiment.