We report on low-temperature electrical transport measurements of single-walled carbon nanotubes (SWNTs) filled in their inner core with one-dimensional cobalt nanoparticles. The electrical transport properties of the hybrid devices are strongly sensitive to the magnetization reversal of isolated magnetic nanoparticles, resulting in strong hysteretic variations of the magnetoconductance. The magnetic anisotropy of a one-dimensional encapsulated cobalt nanoparticle is investigated, establishing an unusually strong dominating contribution of magnetic surface anisotropy.