I'm not sure I'm in the right here, I'm not a mother and I'm only 23. But have you thought about simply trying to explain depression in simple terms to your child? I know we like to protect children from "inappropriate" things but it can hurt just as much to be too shielded and lied to (even if for the right reasons). Your child seems to be smart/aware/old enough to realize that something more than an ear infection is going on so maybe she could understand something like this:

Hey, I wanted to talk to you about something I found out about at the doctors. I have something called depression, its a disease that makes people really tired, sad and *insert some of your symptoms here* - so I'm going to be home sometimes. You don't need to worry about it, it just makes you sick more often and need to rest.

Try comparing it to something they recognize - like having a cold but really often, or something your child has actually had before so she can try to understand.

Obviously word it like normal but maybe a simple explanation... would you tell your child if you had really bad arthritis? How would you explain that to her? What if you got (these are basically no chances but it's a similar disease in some ways) mono? Or broke a leg?

sorry this happened - I myself would feel HORRIBLE THAT my child felt that way =(