The correct choice regarding the effect of the conditional mood in the sentence, "If my dog is feeling better, I could take her for a walk," is that it expresses uncertainty or possibility. The speaker is indicating that the action of taking the dog for a walk is contingent on the condition of the dog feeling better.
So, the best completion of your response would be:
"It expresses uncertainty about the future action of walking the dog, which depends on the dog's condition."