Every living thing is created from a spiritual substance which is referred to in the LDS Church as intelligence. This substance from which all life was created by Heavenly Father is eternal, every living thing from mankind down to the smallest microscopic organism, has a spirit.  
 
All these things will be in a perfected state of peace and immortality after the Morning of the First Resurrection, so yes you pets will be with you in the afterlife. The only difference between man and other animals is man can become exalted and inherit the glory of Heavenly Father and Jesus Christ, while other creatures cannot obtain this glory.

Thank you for your comment. I have been thinking alot about the LDS faith and this is one more positive aspect.

I was always taught that our pets will be able to choose whether they wanted to be with us; based on if we mistreated them or not. 
So be nice to your animals! :)