Under most contexts, it should be "what will we have to do for tomorrow?" "Would" should only be used if
(a) You're using the past tense of "will"
(b) You're talking about something you repeatedly did in the past
(c) You're talking about something that might happen (the conditional form).
The only possible scenario that applies to this sentence is (c) since you're talking about tomorrow and not the past. If there is uncertainty in what you are to do tomorrow, you'd use "would" instead of "will."
I hope my answer helped. Please let me know if it was unclear.