Good digital compact camera with no delay to photograph my kid?

I need a new camera. I mainly take pics of my child, but the delay on the camera I have is really slow, and she's moved by the time the pic is taken. Any recommendations?

The so called shutter lag has gotten much better with new cameras. A lot of the delay is now gone. New cameras also perform much better in low light. This means that you can use faster shutter speeds and reduce motion blur, as well.
But there are two other limitations that do still exist:
New cameras can still take over a second to focus. If you pre-focus (half press the shutter button) while you compose the shot, performance will improve immensely. You can do this with your current camera too, of course.
And new cameras still work with electronic viewfinders. The viewfinder itself is also a tiny source of delay. It drove me crazy with my compact, because you always have to anticipate the right moment. Eventually I got so frustrated that I bought a digital SLR. (Digital SLR's don't have this.) The trade off with digital SLR's is that they're bulky and expensive.
With compact cameras, I really like the new stuff from Panasonic and Canon. I can second the sites that Bruce_MA provided for great reviews.

You are referring to what is known as shutter lag. Most cheap camera has this problem. When you buy a new camera, make sure you look up the spec on shutter lag. I usually go to places like www.dpreview.com or www.steves-digicams.com for review.

Canon PowerShot S3 IS - Great picture quality and fast response. If you want a lighter camera and don't care too much about zoom, try PowerShot A700.

Kodak EasyShare V530. This camera works wonderful. If you'd like to see some of the pics I took with mine, just e-mail me. Thanks and good luck.

Cannon Digital IXUS 550 and up. You'll love the small metal case, large screen, and very fast shutter speeds. (Ideal for fast moving little blighters...) Even records video clips...

Canon Rebel XT 8.2 megapixels SLR will solve problem immediately but camera is pricy. $700-$1000 with lens