On a general note: It helps you and others if you provide a translation (using hide details), so everyone can check whether they can read your sentence and can give you more helpful Feedback.
More specifically towards your sentence: I think that using two case marking particles is a little bit confusing, as now we don’t know whether the dog or its fur is the subject of the sentence.
I believe using a second の instead of the はwould have been better.
Also keep up the good work.