How do I say I took the dog for a walk- using se promener as the verb

Susan, here is the lesson you need to read. The site can be searched. 

French makes a distinction between ‘walking something’ and walking yourself (accompanied by something). 

I wouldn’t use ‘se promener’ in the sentence you pose - it is unnecessary and changes the meaning. 

Where did the question come from ?

 Expressing "to walk" with se promener/promener/marcher/aller à pied in French