fxtrtr,
There are quilters who do their applique & quilting all in one step. Whether that would work for you depends on how densely you plan to quilt it and how secure you want the edges of your applique. Over time, the more secure that 1/8" from the raw edge is, the less likely it is to fray (some people like the fraying -- it's a design choice). The most secure is to enclose the edge completely by turning it under before stitching. The second most secure would be to use a fusible web that goes in 1/4" from the edge on the back and then is satin stitched to the background. Third most secure (still almost never frays) would be to do fusible with a close blanket stitch or decorative stitch that mostly covers from the edge 1/8" into the applique piece. After that, the more spaced apart your stitches, the less they cover the edge inward, the more likely it is to fray. Fusible will slow down and reduce the amount of fraying, but with washing and handling, over time any edge not enclosed or securely stitched to the background will start to peel up and fray.