Answer: happiness and peace.
Step-by-step explanation:
This phase of "new existence" Buck romped through is happiness and peace, because it's suggested that he went through great ordeal throughout his convalescence and after so much pain, he simply entered a phase of peace and tranquility that appeased his soul.
The verb "romped through"is indicates that Buck transitioned and broke through. It's a strong verb, which points at a significant change in Buck's state of mind and spirit, so this must have been happiness and peace.