I am a psychology major, and I plan to get a PhD. My school (for undergrad) doesn't have a live animal lab. Some schools do, but I am not sure if it is mandatory that you do research with animals. If you are looking more at clinical or counseling psychology (where you do therapy, diagnose psych disorders, etc.) then the chance that you will have to do animal research is very slim.
Das_nut gave very good advice about calling the schools and asking them. There are even many graduate schools that do not have live animal labs at all. Just look into it, and good luck!