take her to see a counselor sooner rather than later. My now 14 yr old dealt with some serious issues that I didn't take her to a counselor for - until 3 years later when she was in such a deep pit that it's taken a while to get her out. Unfortunately it's tough to find pediatric counselors - and if you're in an HMO you may find that the network counsleors and not good at all. We ended up spending a lot of our own money to get her to a good counselor who has worked wonders. At age 9 your daughter will probably want you to sit in on the counseling session. that's good - you can use your own judgement and gut feeling to determine if the counselor is good. Some have ideas and world views that will be very different than yours - do not take your precious treasure of a child to someone who looks at the world differently than you do. For us we wanted to find someone who shared the view that there is a God who cares intimately about you and wants the best for you. Having someone speak these truths in to my daughters heart & mind was of primary importance.
Although the school counselors are not bad - we'be met some great ones over the years - you'd really be best served finding one outside of the system. Their ultimate goals will be different than yours as you're looking for your child's look term health - and they work for the school district so they're looking much shorter term - and they are generally overwhelmed as it is.
Depression comes in all sizes and varieities - there can be brief bouts - where the brain chemicals are off kilter for a few weeks. This is a different world than the one we grew up in. At age 9 I don't think I even knew what suicide was - but we're raising kids in a more scary, less secure world. Be sure to let her know that you love her dearly and that no matter what you're doing or how busy you may be or how crazy your schedule that you will always be three and you'll stay up all night with her if that's what she needs, etc. It will give her a sense of security that she may really need at a time like this.
And pray. I truly believe that God cares about the details of our lives. Jeremiah 29:11 says " I know the plans I have for you declares the Lord. Plans to prosper you and not to harm you plans to give you a hope and a future." Ask that God gives you discernment about her heart and mind. Ask that God would show himself to you and to your child and that she would feel his peace.
Finally consider that there may be a child at school who is dealing with a tough issue and is bringing the emotional baggage to school and somehow influencing your child's thoughts. Have a talk with the teacher to find out if she's sitting near someone or spending time with another child whose going through a tough time. Kids pick up on other's problems and they don't even realize it. Knowing what you're dealing with can help tremendously.
Bottom line - it's so worth your time and money to invest in your daughter's heart and mind right now. We realized that counsleing was going ta cost us a small fortune - but we decided without hesitation - that our child's mental helath is more valuable than a new TV or a nicer car. You can't allow her to have these worries and concerns without helping her address them and change her thinking. We're just not equipped to deal with this stuff - unless we have a psych degree. Thankfully your daughter knows she can come to you and talk about this stuff - it's scary for her and she wants the security that only her parents can provide. You'll be her rock - and get through this and look back so glad that you took action to help her through this time.
This parenting stuff is way more difficult than I ever imagined!!!!