Structural, optical and magnetic studies have been carried out for the Co-doped ZnO nanoparticles (NPs). ZnO NPs are doped with 3% and 5% Co using ball milling and ferromagnetism (FM) is studied at room temperature and above. A high Curie temperature (Tc) has been observed from the Co doped ZnO NPs. X-ray diffraction and high resolution transmission electron microscopy analysis confirm the absence of metallic Co clusters or any other phase different from würtzite-type ZnO. UV-visible absorption and photoluminescence studies on the doped samples show change in band structure and oxygen vacancy defects, respectively. Micro-Raman studies of doped samples shows defect related additional strong bands at 547 and 574 cm(-1) confirming the presence of oxygen vacancy defects in ZnO lattice. The field dependence of magnetization (M-H curve) measured at room temperature exhibits the clear M-H loop with saturation magnetization and coercive field of the order of 4-6 emu/g and 260 G, respectively. Temperature dependence of magnetization measurement shows sharp ferromagnetic to paramagnetic transition with a high Tc = 791 K for 3% Co doped ZnO NPs. Ferromagnetic ordering is interpreted in terms of overlapping of polarons mediated through oxygen vacancy defects based on the bound magnetic polaron (BMP) model. We show that the observed FM data fits well with the BMP model involving localised carriers and magnetic cations.