At what level immunity can you force an attack on doomsday tile and win?

This will depend on the strength of your APC and the level of the plot you are attacking. If it is a high level plot (12+ for example) you will need a lot of troops / hero skills and preferably upgraded Fortress buildings to give you a chance of winning.

For low level plots and a strong attacking force you can win with an immunity deficit of 300 or more. For high level plots you will loose a lot of troops and any fight with a deficit is a risk. If you are maxed with heroes skills and troops then you can win with a small deficit.