Our son is 11.5 as well and I also perceive depression in him. On a bad day, he is very negative, is convinced no one likes him, can see nothing positive in his life, and even asks what's the point of life? But he is very changeable. He often goes the full range of emotions in mere hours, from happy glee to raging anger to morose sadness.
I've noticed some of these behaviors for years and we're finally going to a family therapist. I have depression and that can affect the dynamics of all of us. We also have some marital issues that compound things in our parenting styles. Some of his issues are how we, as parents, deal with each other and/or with him; some are his issues on his own. So, it's a full family thing. That may not be so for you, but it might be something to consider.
One piece of advice I would offer is that the best time for our son and one of us to talk with him is at bedtime. He's relaxed and pondering life as he waits for sleep. Sometimes we have the best conversations at those times. Those times are a real gift for connection!
You might find that something in particular is bugging your daughter. She might be thinking about her maturation process, especially with a new baby in the house. Hormones may be wreaking havoc with her and she may not understand what's going on. She may notice the effects of depression and anxiety in you and not fully understand it. The sky's the limit for what might be bothering her right now.
My only caution is that I'm a talker and our son is not always. It can be a fine line between asking too many questions and not enough. Catching him at the right time is the key. But sometimes you just have to dig in, even when he doesn't want to talk, and you find a whole world of concern in there. Trust your gut and share some of your experiences and feelings with your daughter. It might be the window to a whole new world for her that is very helpful.
If you find you can't handle it yourself, a school counselor might be helpful or even another professional outside of the school. One reason we're doing the family counseling is that we don't want to give our son the impression that HE is the problem. We're all in it together and all could use a little help in expressing our feelings and concerns.
Best of luck and peace to you, your daughter and your family!