“Si” does not call conditional in French. There is a very famous incorrect sentence “Si j’aurais su”, used to convey childish incorrect language.

And yet, in your example, both “devait” and “devrait” would be correct, but would not have the same meaning.

The version with “devrait” is about going outside in the future. In French the conditional mode is also used as future in the past, without conditional meaning. Please note that the same applies in English: a sentence like “I hope it will rain”, put in the past, will become “I hoped it would rain”.

In French, here are the two possibilities, with present version and past version:

• (present) Elle se demande si elle doit => (past) Elle se demandait si
  elle devait
• (present) Elle se demande si elle devra => (past) Elle se
  demandait si elle devrait

I think your original sentence in English corresponds more to the first version with “devait”. Not sure how to say the second one. Maybe “She was wondering whether she would need to go outside or stay indoors”…