Love your beautiful block! You hand pieced it? Wow...
You absolutely can quilt it as you go. I did that with my Boom swap blocks and posted a tute on the method I used here on the board. You may want to take a look and read through it so you'll feel confident in that method. There are many ways to QAYG, but this is the one I used. It will have a narrow (1/2") sashing when you are through.
http://www.quiltingboard.com/tutoria...l-t283918.html