extending the life of kids' pajamas

My son has outgrown a pair of well-loved pajamas.  I'd like to extend the life of the shirt by removing the graphic and then stitching it onto a larger shirt.

Will double-sided fusible webbing work on jersey knit material? 

I actually don't mind if the edges curl a bit on the perimeter of the design. 

Will the webbing stabilize the fabric AND help to anchor it onto the larger shirt?

Is it necessary to use a zigzag stitch or would a straight stitch suffice?

Thanks so much!

Yes, the double-sided stuff should work to keep it on the knit. A straight stitch would be fine as well. I've used both and haven't seen a significant difference to advise one over the other. The only other advice I would give is to be sure to let your webbing cool before trying to work with it. It tends to not stick if you try to move it too quickly after ironing.