Doomsday has withstood things alot more powerful then that beam and his claws can hurt energy beings i dont think the destroyer would have much luck.
Doomsday servived Omega Effects which can hurt the spectre and the anti-monitor.
Doomsday came back after being destroyed by Imperiex making me think he can take the blasts now.
He took blasts from a gog that could totally destroy superman with ONE blast and didnt die but was still alive through out the entire battle.