I spent 14 months recently volunteering at a local shelter, not the one in my county but adjacent. Since they all are run completely different from each other and because they usually have very low morale, and often not very good PR, I would suggest volunteering in whatever capacity is advertised as needed first. Then get to know how the place is run.

As a rescue veteran of 10 years or more, I have come to know all the shelters in my state and some adjacent states fairly well. They are usually leery of someone until the volunteer turns out to be reliable, dependable, etc. Do they already have a photographer even if amateur? The shelter I was at already had a retired lady doing this and it is her life. She does a great job. However, there were some animals that she never photographed and those were the ones I went in and photographed and personally handled all of those adoptions. So see what kind of photographs they have of their animals now and if that position is most likely filled already, which is often the case.

Good luck!