What can still be done a week before the JPLT… Instead of memorizing new grammar or words, I think that doing drills is the best thing one can do. It is a way to study again the grammar and expressions already learned and getting more familiar with the tricky questions of the JLPT. It works well for the grammar part, seeing again and again similar pattern helps memorizing the grammar you don’t usually use.
And don’t let your cat discourage you!