Past perfect or present perfect?

They're both correct, but they mean slightly different things.

It seems to me the best answer would be

... because we had a fever.

This says that you had a fever last night, but doesn't say whether you had a fever before last night, or whether you have a fever now. That's all the information you really need to convey.

Both the alternatives work, but carry more information:

... because we have had a fever.

This implies that you still have a fever.

... because we had had a fever.

This implies that you had a fever before (possibly including) last night, but that you are probably over it by now.