The likelihood of asbestos in this plaster

Often, people talk about “old-fashioned horse-hair plaster,” but the binding agent in old plaster walls was more commonly cattle hair. -searshomes.org

I am reasonably sure it's not asbestos.

Nobody can tell you whether or not that is ACM (asbestos containing material) by the pictures. You have to send it to a lab to know for sure.

Does it look like other ACM I have encountered? Yes

Will it hurt you if you wet it, bag it, and throw it away? No

Could it hurt you if you keep it laying around on your desk taking pictures of it and handling it? Probably not, but you should throw it away and stop stressing out

It takes time (think repeated/prolonged occupational exposure) for adverse health effects due to asbestos exposure.

Dust would be your biggest concern, especially for children. It is in what is called a friable state, meaning easily becomes airborne and inhaled. As a precaution, in the absence of lab results, it should be handled wet, like moistened with a water spray and mopped up while wearing a particulate respirator (a regular dust mask is not recommended). Alternatively, it can be vacuumed using a HEPA filter with the aforementioned respirators. Wear disposable coveralls (we use Tyvek™) and bag those and dispose as well. In the U.S.A., for confirmed ACM, this activity is regulated and may only be performed by specially trained and licensed personnel due to likelihood of repeated occupational exposure, and the waste is treated as hazardous.