The structure do sth. to be worthy of is used here. sth. in this structure is the object, and the infinitive is the postpositional attributive of sth.
This sentence is an interrogative sentence, and the interrogative pronoun referring to sth. is advanced to the beginning of the sentence, specifically changing into the following structure:
〔Object in advance] What
〔Subject] we
[Predicate verb] should … do
[Separating attributive] to be worthy of the age we Live in (where we live in is the attributive clause of the antecedent age, omitting the relationship as an object Pronoun)
Translation: What should we do that is commensurate with the times in which we live?