Depression is definitely one of the most difficult obstacles to face while in a relationship. The severity of the depression can affect how important it can be. I would date a girl most definitely. It doesn't matter to me. But I kinda have a lot of experience with the topic. If the guy is mature enough then it can work out.
Sure, you can still date. You will need to be selective, though. It will have to be someone mature and/or someone who has had experience with depression themselves. Preferably someone with 'references' from people you know.
We ALL have problems and there's no reason to think you're a pariah. A lot of people, maybe a third of the population, have suffered periods of depression. Talking to others is good therapy. But you will get along better in general with other people who have that tendency.
I'm sure by now you have at least an infomral network of people who can relate to your depression. Try making a conscious effort to date within that group, maybe AS a group at first. Dating as a couple might be difficult until you already know the other person through group activities.