Do you have to have a college degree to be a police officer?

No .. Check the link below for the process.

http://www.learnhowtobecome.org/police-officer/

Sometimes. There are a few depts that require an Associates degree. Others require various number of hours. (30-45). Some don't require any.
Law enforcement depts. are always short on the number of female cops they have, so they actively recruit women. If you have a good background check and are physically fit, you will have no problems getting in.
However, understand that many female cops do not stay in the field, and, from what I saw, many who left went into nursing. I think it is because we, as women, want to "make a difference." yet, once we are in, we realize that it's a lot less social service oriented than we expected.

What do you mean if veterinary "does not work out?" Even if you cannot get into vet school, there are other vet-related jobs, such as vet tech. I don't know what they pay, but some do a lot of work. I live in a large city, San Antonio, where we have a veterinary specialty hospital. The vet techs here are awesome! http://www.vrecsa.com/services.htm

Of course, any background in animal sciences would help prepare you to be a K9 handler!