Do you think I'm shallow if I don't want to date someone diagnosed with depression?
I think you might be. Why don't you want to date someone that has depression?
I think the relationship will be very challenging and I don't think I can handle it.
Dealing with people who have mental issues can be difficult but you shouldn't judge them for that. It is something they can't help and can take time to learn to manage. It is something they can also develop after you start dating or get married so you will have to deal with it anyways so you should be considerate of their situation.
Maybe I'm selfish but I don't think they would be emotionally available to me because of their mental health.
If you find someone you deeply love, their mental and physical health shouldn't be a barrier to a relationship. Open your heart and it will help you to find love.