Is travel outside of belgium allowed without a Belgian ID?

Yes , within the schengen visa validity date

You said you are a non EU national therefore you will not receive a Belgian ID unless you are Belgian as well. As you say you have a work permit, that is evidence you are not Belgian. Belgian IDs are for Belgians.

If you have a valid Schengen visa, as said above, you can travel inside Schengen.

Check carefully that your visa does in fact cover the whole Schengen zone and not just Belgium, if it is it will state "all schengen countries", probably in French or Dutch. Visas issued for work purposes are usually country specific for obvious reasons. This wouldn't be a significant problem if you were travelling by land but flying airline officials will check your status before you are are allowed to board and if they are not satisfied you won't be allowed to fly.

Your commune should be able to give you precise information.

"Would I be able to take a domestic flight to another country try in Europe" (sic)

No - You can fly to other countries that are part of the Schengen Zone.