How to cut and remove sharp edges on aluminum sheet using a Dremel Rotary Tool or other tool?
For material that thin, even a set of heavy duty scissors will work well enough. Harbor Freight sells stainless steel multipurpose scissors for six bucks US that should do well enough for 0.0125" stock.



For the sharp edges, especially in aluminum, a deburring tool should do well for your purposes. A quality tool will be somewhat expensive, but there's such a large price range in this item that you should be able to find something in your budget.



I have a tool similar to that in the photo and use it frequently on aluminum and plastic sheets to chamfer the edges. In your case, such thin material will need support. It may be necessary to place the edge on a solid surface such as a countertop or sharp edged table to provide the necessary support. Deburr one edge, flip the piece over and deburr the other side. 

In the above photo, it appears that the E200 bit would give the best results. Light pressure, drag the cutter along the edge and you would see a curl of aluminum from the cutter. Too much pressure and you'll create a new sharp edge.

Alternative solution involves a hand file and the aforementioned support table or countertop. Push the file downward over the material creating the chamfer as you progress along the length. Dremel-type rotary tools also have burr bits that would work, but with a single speed (high speed) tool such as yours, the possibility of removing too much material is quite high.