Why does my 7 year old say she hates herself?

My 7 year old daughter frequently says she hates herself and also says she doesn't care if she dies. She is a single child and is with me (and my fiance) during the week and with her dad and step-mom on the weekends. I feel she gets plenty of attention from everyone no matter whom she is with so I don't think she is saying this for attention. I am worried this could be early signs of depression. Her teacher this past year did notice she has a low self-esteem and I have been trying to praise her more often. It's almost like she does things she knows she shouldn't do (like toss the cat or throw toys in the house) but then says she is 'so very sorry' and is extremely hard on herself after wards. She has even put herself in time out a number of times over little things.... we don't even use time out at my house. She is a very emotional child (always has been) and I have tried sitting down and asking her if something is bothering her when she gets upset but she always says she doesn't know. Any advice on how to handle this? I have already talked to her pediatrician but that didn't get my anywhere. She has been seeing a counselor (monthly) since December but it doesn't seem to be helping much