I'm looking for one to build a MS-paint like app.
OpenGL is for making 3D applications. Using it for pixel-based things like a paint program will make things very hard.
The closest thing I can imagine is to paint the pixels for the ellipse to texture surface and then show it as sprite. Be sure that you always have identity transform set, otherwise the result may look blurry.
A good alternative for OpenGl in your case would be SDL. It is simpler and pixel based.
Bresenham's drawing algorithm is used to scan convert the ellipse, i.e. correctly draw and fill the edges of it. OpenGL is a polygon based graphics library that does it's own scan conversion, so I'd say you are thinking of doing it the wrong way.
Personally I'd calculate some points round the edge of the polygon, e.g. by regularly stepping from 0 to 360 degrees and then draw a GL_FAN with the center as the first point and the calculated points as the rest (and including the 0 degree point again at the end).
This will not be perfectly accurate, but good and fast for most purposes.
You could be more sophisticated and generate more edge points if the ellipse is larger, which will improve the accuracy.