It is extremely risky to wash a quilt top that is not quilted. Fabrics can shrink at different rates and pieced edges can fray. It can result in a real mess.
Since this quilt is already partially quilted and the edges are covering the batting and sewn down, I would wash it before taking it apart. Before washing, however, I would run large basting stitches (by either hand or machine -- do not need to be neat!) in any open areas that are without quilting. This will help stabilize the top so fabrics can't shrink apart from the batting. Once quilted, the three layers become one and batting takes control of shrinkage. This means that no fabric is allowed to shrink more than the batting.
With a quilt that large, I would take it to the laundromat and use their largest front loader with Synthrapol (widely available on Amazon and in quilt stores that cater to dyers). I probably wouldn't use hot water, but rather cold. Even with cold, the Synthrapol should prevent any dye bleeds from settling into the fabric. I would partially dry in the laundromat dryer, then bring the quilt home and lay out on carpeting (or outside in the shade to protect from sunlight, on a flat sheet with another flat sheet on top to protect from birds flying overhead) to finish drying. Inside, aiming some fans on the quilt will speed the drying.
Only after all of that would I take the quilting stitches out and separate the layers.
Edit: One more thing. I would add about 1/4 cup of this:
http://www.amazon.com/gp/product/B000TSO20W/
with the Synthrapol. This stuff is amazing in terms of soaking up "off" odors in laundry.