Yes, it's a phrasal preposition that means except (Merriam Webster).
We can use 'suffer' if there are any modal verbs before it; could is a modal verb that takes the present form of the verb coming after it, as in:
- “She could not do anything about her bad luck other than suffer through it.” [see 'do' and 'suffer' following the modal verb could. Using doing and suffering would entirely be ungrammatical here.]
To consider your example more analytical, you can say:
- “She could not do anything about her bad luck, but (she) could suffer through it.”
Thus, don't say 'doing' or 'suffering' like this:
- “She couldn’t doing anything about her bad luck other than suffering through it.”