k i'll help u out here with the shutter lag. afterall i started off with compact photography. (: only went dslr cause i wanted to have greater control.

as for ur shutter lag problem, learn how all professional photographers shoot: be it dslr or not.
u pan along the doggie movement. not just simply prefocus cause its not enough. follow the movement of the doggie. u will get tat shot. a lot of times i shoot ppl running for ball or ppl running pass me during sports meets, i usually run with them(: