It is against WHO advice.
www.who.int/news-room/q-a-detail/q-a-children-and-masks-related-to-covid-19
"In general, children aged 5 years and under should not be required to wear masks. This advice is based on the safety and overall interest of the child and the capacity to appropriately use a mask with minimal assistance. There may be local requirements for children aged 5 years and under to wear masks, or specific needs in some settings, such as being physically close to someone who is ill. In these circumstances, if the child wears a mask, a parent or other guardian should be within direct line of sight to supervise the safe use of the mask."
If you think your child has the capacity to appropriately use a mask with minimal interference and you can keep them in direct line of sight at all times to supervise the safe use of the mask, rock on...
There's no way I would want my young child wearing a mask at nursery (which is where it would be most useful) without me there to supervise because it impedes breathing and can be dangerous for young children if they can't remove it themselves. The nursery staff already have a lot on their hands...It is not beyond the realms of possibility that they might fail to notice a child in distress hidden behind a cloth until it is too late.
Also, I'm not meaning to be rude, but your suggestion seems a little odd given you have a young child. Do you not understand what children get up to at nursery and pre-school? My DS does singing, reading, running races, climbing, obstacle courses, playing chase, crawling through tunnels. And the nursery staff talk to him as much as possible, asking him about what he is doing and trying to communicate with him. The speech of young children is indistinct enough without muffling it through a mask. And these are all activities for which the mask would need to be removed for safety or practicality reasons (along with for snack time, lunch and drinking water). You'd end up with a whole load of unsanitary, germ-ridden masks littering the place.