I have never used your particular camera and I don't use Premier for editing so I was reluctant to offer advice BUT as no one else has offed any, I thought I would throw in some general tips which may help.
Firstly, well done for recognising you need to use the camera in manual mode. This is often the best way to get a better image. Your camera, I believe, gives you good manual options. So get use to the different settings available to you and try them in different conditions. eg indoors and outdoors etc. The next advice is to get some sort of support to keep the camera steady. A tripod would be best for this with a smooth fluid head or at least a mono-pod. If using a tripod switch off image stabilisation on the camera.
When it comes to image quality apart from keeping things in focus the bit-rate is important. ie the higher the bit rate the more image information the camera is recording. Shooting with the highest resolution ie 1920 x 1080 with a frame rate of 50fps for fast moving dogs, for the UK (PAL) format and then setting your editing software to match these same property settings and matching them again with the final rendering will give you the best results.
This is not always possible for your final render, for example, if you are making a Standard definition DVD but I would keep the highest quality settings until it comes to the final render. When you make the DVD set your bit rate to around 9Mb as this will give you the best image possible but remember you are lowering the quality from HD to SD so there will be some image quality loss.
Hope these general points help in some way.