I have done this three times. It is a real pain but it can be done and you'd never know it. The first one was a quilt I had made for my son and he got a larger bed, the other two were twin size and when I got the newer thicker mattresses they barely covered them.
What I did was take the binding off, make the addition top, batting and backing. I did each side and then the ends. I first put the backing on, then butted the batting and whipped stitched it,(I laid the new batt on top of the old and cut it so it met perfectly) and then added the top fabric.(I moved it up a half inch or so, so I wasn't sewing in the previous seam) They look fine but I swear it would have been easier to make new quilts. The twin that I made into queen size actually looked better. I had several borders on it but they were thin and the old entire quilt fit the top of a queen size bed then I added the new borders and they were wider and framed the original. I had a little problem finding fabric that looked like it belonged since it was all in dark green and cream .Every year it seems the basic colors have a tint that is just a smidge off of the previous season and this quilt was 8 years when I reworked it. He loved it and still does so it was worth it. If you just have to make it longer, it will be so much easier. Good luck.