is it possible to make an invincible floor trap?

Of course

it wont let me edit the properties for it if i place it as a doodad, and if i place it as a unit, i dont know how to enable it

It should be enabled by default.

Make sure the owner is the enemy when you place it as a unit.
You can also use the trigger action set invincibility to make it invincible after map start.

set doodad state can be used on any unit. Floor traps are actually units, not doodads, though they can be placed in the doodad layer. Doodads are nothing more than terrain mixed with a sprite. Disabling a real doodad does nothing, since it's only a piece of terrain.

Keep in mind, however, that not ALL doodads require sprites.