Psychology is a good way to broach goals of becoming involved in animal sentience/behavior and ethology. Biological and zoological sciences of course are also just as applicable, but as far as psychology goes, I would fill your undergraduate curriculum with as much animal physiology and ethology courses as your university provides. However, do not be discouraged if they do not offer many, for comparative psychology and ethology are still up and coming majors. Other than building your animal-focused curriculum, I would get involved in several volunteer positions pertaining to your specific interests in ethology, and assuming you plan on pursuing graduate education after undergrad, I could also provide you with my own research on schools that offer comparative psychology/ethology programs that hone in more on the scope of what you want to accomplish (I am pursuing this path myself).
You will want to get a bachelor’s degree in biology or microbiology. Zoology is also an option. From there you would pursue a masters degree and then a PhD. Your PhD will be more specific such as a PhD in genetics, molecular biology,etc. Different professionals also do animal research: physicians, dentists, nurses, pharmacists, etc. Some examples of research I have been part of are: drug testing in rats, using pigs to learn how to provide better care to burn patients, cancer research, etc.
i apologize, I just realized that you were asking about psychology. That would be your Bachelor’s and Master’s degree field, but take as many courses in biology/ zoology, animal behavior as you can. I forgot to mention that veterinarians also do lab research. In addition most labs that do a lot with animals have at least one vet on staff.