Point and shots are not the speediest cameras, especially in low light. When using it, make sure you pre-focus by half-pressing the shutter.
A feature that could help improve things is optical image stabilization.It helps stabilize the camera when taking photos, however it doesn't stabilize a subject such as a moving dog. But it will give you a bit more advantage when shooting in low light and it can help if your hand shakes a bit while taking photos.
I found a few digital cameras with Image Stabilization in your price ragne. Where the information is available, I've listed the speed for Continuous mode, also known as burst mode, where you can take a series of photos in fast succession. something you might like to try when the pets are jumping around.
Canon PowerShot A1100IS (continuous mode 1.1 frames per second)
Sony Cybershot DSC-W220 (1.7 fps)
Canon Powershot A1000IS (1.3 frames per second)
Olympus FE-5010; Olympus Stylus 7010
The better the light when photographing pets, the better the photos will be and the faster your camera will respond (if you pre focus as mentioned above). Your camera will do better in low light if you shoot at wide angle, instead of telephoto, because the aperture is wider and lets in more light. You can always crop an image when editing.
Here are some tips on photographing animals. As the article points out, try to avoid using the flash.
http://www.digicamhelp.com/how-to/people-pets/photographing-pets/Once you get your camera, you will simply have to practice.
btw, Canon digital cameras have a
Pets and Kids scene mode which is selects a higher shutter speed and other settings optimized for photographing children and pets. I'm not sure if the other cameras have a similar mode.
If you have more questions let us know, even after buying your new camera. Good Luck.
