This easy-to-make threading toy addresses that problem: it's safe as well as easy to handle for the smallest of hands. I first gave it to my son when he was about 18 months, though you could try it at any point between 16 and 24 months. Best of all, it only takes about 30 minutes to put together and uses mostly recycled materials.
You will need:
a sturdy cardboard tube (an empty cling film or aluminium foil roll works best)
a 30-40 cm long stick (wood, bamboo, plastic - any will do)
thin, flat cardboard (e.g. an empty cereal box)
parcel or gaffer tape
1. Using a bread knife, cut the cardboard tube into 1.5 cm wide rings.
2. Using scissors, cut a circle with a wider diameter than the rings out of the flat cardboard.