Well it can be a real concern -- most states treat pets as "personal property" but more recently some states have awarded joint custody, visitation, and even alimony regarding the custody of pets. I believe only Alaska takes into account the well being of the pet. How it's handled will depend on your state, so if this is a leading concern for you then I highly recommend you do a consultation with a lawyer about what you're trying to achieve and what you should do in the near term.
Generally, people have all kinds of preconceived notions about what they're entitled to going into a divorce, but most of that is based on emotion or what they've heard from other people instead of actual fact. Both my lawyer and my sister's lawyer said that the vast majority of people pretty much land in the same place, the only thing that varies is how much money they burn on the way there with their fighting. You're much better served if you can work something out between the two of you and just have the court rubber stamp it.
No need to fight that battle today however. Talk to a laywer, most will give you a free consultation. Getting educated is always a good thing.
Acc
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015