Some photographers complain about the delay from the time they press the shutter and the time the camera actually takes the photo, i.e. shutter lag. If this is an issue for you, consider re-examining your technique before changing the camera.
Shutter lag in recent digital cameras is actually minimal. What many casual photographers consider as shutter lag is actually focus lag, meaning the delay caused by the camera attempting to focus on the subject. Focus lag, however, can be reduced dramatically by half-pressing the shutter to focus before you intend to take the shot. For example, if you're taking a shot of your child running toward you, prefocus (by half-pressing the shutter) on an object that is at the same distance where you expect your child to be when you take the shot. Keep the shutter half-pressed until your child reaches that spot, then you press the shutter all the way. When half-pressed this way, even my old point-and-shoot (Casio Exilim EX-V7) has a shutter lag of just 0.05 seconds.