Nose gear should do just fine. Friend hit a deer with 727 nose gear. Hit it right at rotation and weren't sure if they'd hit it. Retracted gear and flew to destination. Found parts in wheelwell after landing.
Looks like a flaps 40 bounce followed by an abrupt roll. 737 with flaps 40 has known control sensitivity. It's been known to rear it's ugly head when people get startled or have to make last second corrections.
FDR will show if control inputs at touchdown, or during the bounce, were at the heart of what happened.