Debbie B is right - bipolar has a strong genetic link, and yes children can have it. It's going to be very difficult to get a diagnosis at the age of 2, but you know in your gut when something's not right with your child.
Finding a child psychiatrist is difficult. Children's Mercy behavioral clinic has a 6-month waiting list most of the time, and I think you have to have a primary doctor's referral for them to even call you back. We have a psychiatric nurse practitioner for my son, and also an excellent children's therapist I would be happy to recommend. They are in Overland Park. The psych is not over-diagnostic-happy to label your child, and she is very easy to talk to. Both of my boys see her as well as myself.
My 8 yr old son was diagnosed with bipolar in January. I knew something was different with him from age 2, but people would say "oh he's just a boy" or "oh that's how 2-year olds are, you were just lucky with the first one so you think this one is odd" At age 2 he grabbed a knife from the dishwasher and chased his older brother through the house. He would wake up and immediately start screaming "stupid" and "shut up" (the only bad words he knew at the time). He had severe separation anxiety - I never could leave him in the church nursery. He would wake up in the middle of the night, crawl in our bed and try to wake us up, wanting to play. He would stay awake for hours at night, playing in his room, and still wake up ready to go.
If you really feel in your gut that something is not right, go check it out now. There is evidence that the earlier the bipolar cycles are controlled, the better long-term outlook for that child. Also, if she starts school without the bipolar diagnosis, they're going to tell you she has ADHD. If the doctor you go to doesn't recognize the differences between ADHD and bipolar, your daughter will be put on stimulants that will make the bipolar worse.
If you'd like more info, you can e-mail me at ____@____.com or check out www.bpkids.org
Best wishes