Two cautions specific to this being a soft toy rather than a loose part.
Protect the fabric. Abrasive slurry and polish will get into the plush around the eye and it is very hard to get out. Mask the area with tape and a slit card around the eye before you start, and change it when it gets loaded.
Test on the less visible eye first, or on an inconspicuous edge. Plastics vary and some react badly to solvent-based polishes — clouding or crazing that appears minutes later.
Also, work in short sessions and look at the result dry. Wet plastic always looks fixed because the water fills the scratches, which is exactly the illusion that makes people stop too early or keep going too long.