That is an excellent idea. Go in an ask what his expectations of you are and tell him what you want to achieve by attending. Therapy is hard to do for a lot of people but it seems that you have a lot of insight into yourself and a true desire to get better or fix a problem.
I know that sometimes I feel that I sabotage my own treatment due to not being as honest as I can be or forthcoming in therapy. Once again this is due to my career field and worrying about being "caught up in the mental health system". I really have to work very hard not to do this. As I know this thought process is irrational and nonproductive for me, but sometimes....
Maybe you can make a list of things you do want to talk to him about and stick to it. If it is an anxiety issue there are breathing exercises you can do that help and medication for anxiety if indeed this is the problem. Your Psychiatrist is going to want you to be as descriptive as you can be about how you feel and what is going on in your life that can effect your mood and or possible reasons for depression.
Also, the thing with the pet he was probably saying or referring to the fact that statics show that animals have a healing and uplifting effect on people. Our psychiatrists recommend to patients who dont have animals to get a cat or small dog to help with their mood or depression. I know my cat Normandy helps greatly with mine.
Anyway, I dont feel that I have helped much here and I am sorry for that maybe someone else with a much more brilliant mind will come along and post some ideas. I hope that you do continue to post here, we are happy to have you and your input. Take care.... and let us know how your appointment goes (if it was any better)