I think what you're asking (aligning the verts) is simple. Before you duplicate half of the dog, goto the front view. Then select all of the verts that you want to align. Once you have them all selected, use the scale tool to align them. If you verts are verticle then you will want to scale them horizontally. Keep scaling until you can't scale no more. You'll know it when it happens.
Step 2: Next press the F8 key to return to object select mode. then press the "w" key. then press the insert key. move the axis orientation to one of the verts you just aligned. You can do this by clicking on the horizontal part of it so that it highlights yellow. Then hold down the "v" key while you move the horizontal yellow part with your mouse. Once you have it on the edge of your dog, then press the insert key again. Now (while still in object select mode), select the horizontal arrow so that it turns yellow. Then hold down the "x" key while you drag the yellow arrow to the center line of the grid. Your dog should now be exactly centered on the grid.
When you duplicate, your dog will be perfect and all you have to do is merge the verts of both halves. Sorry but I can't think of what the arrow thing is called.
If I didn't make any sense let me know and I'll explain it better with some pics.
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