Have to disagree with Mike and undertow. Your shutter speed is slow enough for the strobe to fill the scene. I would tend to agree if you had a shutter speed that was faster than your strobe (ie 1/250 or faster) but slow is not usually a problem. See my photo below with same shutter speed both upclose and wide angle (shutter speed 1/100-1/160). I do agree that you should shoot in M mode.
Heres a good intro article to strobe position. I wouldnt position the strobe directly on top of the camera but a little more to the side. Top position gives you better color, side position better contrast, diagonal should be a good compromise. Since you have one strobe try to be aware of the sun and you can use it a second light source (usually also diagonal). Good luck
I have to agree with Atobit. Both pictures are overexposed at the bottom which leads me to believe your strobe is actually pointed down rather than straight or ideally a little bit up from your subject. Try putting the strobe in the 10-11 or 1-2 o'clock position, this way you get both the benefit of color and contrast as compared to top or side lighting.
I got my dog this one for a 5 day canoe trip and he didnt mind wearing it at all. It has spandex at the bottom so they can move freely. Not sure if they have something small enough for a chihuahua. Good luck