1/500th is plenty fast for the dog
Read the manual and learn which focus points work best for you. Bump the ISO to 400 for general stuff, use Continuos Focus for moving things. Leave it in Shutter Priority to start things off. If you try and handle issues with Aperature settings (F-stops) you will screw yourself up. Opening up (lower F #) will decrease your Depth of Field (Dogs nose be in focus and nothing else) You were at 5.6, more then enough DOF to catch the entire dog with the lens your using.
You also have the camera set to focus on teh closest subject, thats why the brick wall is in focus and the cat isnt.
And use jpeg fine...you have alot more quality left in that camera that your holding back!
Best advice, read read read the manual and there are tons of beginner photography sites on the web that can speed you along, most even have videos that help walk you through things. Once you get the hang of it, youll be shooting as good as most on here in no time
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