How stable is that configuration and under what conditions such object may form ? Is there any evidence suggesting that such objects might exist ?
No, such a configuration would not be stable. Matter tends to clump together and as the mass increases the rotation slows.
If the rotation were too fast for the material at any given size then the stresses would be too great for it to remain as a cohesive body. In these cases you would get something more like a rubble pile. If the rotation were somehow sufficiently high enough to theoretically form a donut shape, I think the gravitational force of the matter would not be enough for it to coalesce into any sort of cohesive body.
Consider, for conservation of angular momentum the angular velocity decreases as the distance from the centre of rotation increases. That is, stuff closer to the centre rotates faster than stuff farther away. But for a solid body the angular rotation is the same at all distances from the centre. This means that the angular velocity (in degrees per unit of time) is the same at all distances, and in this case the stuff closer to the centre rotates more slowly than the stuff farther away.
So to form a solid body the stuff in the centre needs to slow down as it accretes matter - it rotates more slowly as it gets bigger. This would prevent forming a donut because the centripetal forces don't outweigh the gravitational forces. Fluid bodies like stars or planets with liquid/molten cores are more complex but the same idea applies.
Simple answer: no.
Shapes like a doughnut (this shape is called a torus) can exist in space, but not in dense material. Dense material becomes spherical because gravity drags it together and a sphere is the smallest it can get (size depends on what is opposing gravity - turbulence or radiation etc.)
The definition of a planet actually involves spherical shape because this is related to size and mass. Asteroids can be made of similar material to planets, and be orbiting the sun, but one of the reasons we don't call them planets because they are not spherical.
COnsider this counterexample: the asteroid belt. Taken as a whole it's toroidal, but only because all the components are revolving about the sun. They wouldn't even form a torus in the absence of their orbital parameters. Larger clumps (i.e. protoplanets) can only form due to gravitational attraction, which produces straight-line attractive forces (as opposed to, e.g., the path of a free electron in a magnetic field). All material is drawn towards a common center.