There's a nice little pattern of "be to (verb)" to signify an expected action. You'd normally find this in future forms such as "I am to be married in September" or "He is to give a speech this evening." You can also use this in present form: "So, what am I to take on this trip?" Watson's example means he doesn't know what they were expected to do. If he used "were going to", it loses the sense of expectation.

"What were we to do?" is nearly equivalent to "What were we supposed to do?" "What were we going to do?" is a question directed toward previous plans. For example, if someone said, "Looks like we can't do that anymore," someone who wasn't aware of the plans might ask,"Well, what were we going to do(in the first place)? Essentially, it describes the progress of action in the past. Let me know if you have more questions. It's slightly difficult to put into words.

Which tow sentences? Where were we going? = Asks about our destination What were we to do? = What decisions we should make, etc. What were we going to do? = Asks about the plans we had previously, but didn't carry out.

This is language typical of the time. Obviously the narrator is thinking aloud and musing on the expedition. what were we to do means - what are we going to do.