Absolutely you can; I was in my 20's before I realized that quilts could be made of materials other than heavy polyester knits and old jeans.
It is trickier to work with knits, so I would keep the pattern simple. I've never tried it, but I don't imagine the corners working out nicely on half square triangles, so I would stick with squares and rectangles. Since you have experience with garment sewing, I don't think it would be beyond your abilities.
Good luck!