Have you thought about one of the folding tables that have a plastic top. I think they come in a 3' x 4' size. If it anywhere near the same height as your desk that might work and you could fold and put away when you don't need it. It may be less expensive than the wood needed to make the drop leaf. I think they are available at Costco, Sam's Club and maybe Walmart, & Target.

One one of the free shows last weekend, the quilter had used two dressers with drawers on either side and put a piece of plywood on top. You might be able to find something that would support the top and use as storage as well, or just add legs, sawhorses, even computer paper boxes on either side for support. Like the idea of putting part on desk and rest on backside that All Thumbs suggested. That would make it sturdier, less likely to separate.

Ditto with Jan's suggestion. Screw a long 1 x 4" along the entire back. Set it a little down from the top of the current desk so when you swing the back up the edge of the drop leaf will cover the added mounting board and be level with the top of the desk. Do add legs to the leaf for support. Better yet- check thrift stores and watch Craigslist or Freecycle for a sewing cabinet, desk or table for conversion. You can find them very cheap or even free. Eleanor Burns has something on her website showing how her son converted a table years ago.

What might be easier is to get a tabletop double the size of your current desk (or more), attach two legs to the far side, and use the current desk as a support for the front half. So the new top is resting on top of your current desk, and is perfectly flat with no seam. You might find a wooden poker table at a thrift store, or a small breakfast table that you could take two legs off of. If it's slightly bigger, like a couple of inches all around, it wouldn't matter.

This is also what I has in mind. And of course you would need legs to support the leaf when it was set up. As for cutting a "hole" to drop your machine in to make it flush with the desk top, yes, it can be done. My DH made one for me. Only mine is in a large leaf that I put in the dinning room table when I need added space. He cut the hole, then built a sort of drawer and used L brackets to attach it to the under side of the leaf. It holds the machine just fine. I used it just today to sew the binding on a queen size quilt. Good luck with what ever you come up with.

Jan is right. The piano hinges are a good idea too. (and Darlene is right about 1-2 support legs, also)

From previous threads on this subject, remember to make the height of the throat plate even with your elbows so you don't get tired shoulders, etc. You could even take those feet off your desk drawers and then cut the two legs off. I just cut 4" off my 1967 machine cabinet. I cannot believe I did not do this years ago. If you can find those plastic drawers or even a 2 drawer filing cabinet cheap, you could put that next to the desk on the right, at a right angle, add a covered top and turn it into an ironing board. I just had another thought, cut a hole in the top for the machine, measure so it fits your elbow height, put a shelf with little "L" brackets, underneath the top, add a piece down the right side so the "L" brackets can be on that side, and that would hold your machine. You could even close the back and side with that gray board, I forgot what it is called, (like pfc board. It is cheap, just a few bucks, but very sturdy. You could even buy a piece of that peg board on the side to hang your rulers, etc. Good luck. Yes, use legs for support and a piano hinge.

I have the sister to your desk. My desk is 4' long, and I used a 30" piano hinge, a 5/8" x 16" x 4" long piece of pine or the cheapest wood in that size, and 2 Gate house Folding Support hinges for the side support. I did not put any legs on it and I have had no problems with it. I have done a king size quilt without any problems. I don't use it for cutting though, if I did I would add legs for more support. I have been using the extension on my table for about 1 l/2 years now. I plan on painting the whole desk and extension when the weather is warmer. I did it all myself so you should be able to do it too, If you need to cut the wood, the people at Lowes will cut it for you. I would like to add photos, but can 't figure out how to add them

Having vision and imagination go with quilting 101. I don't think the person at Home Depot has the vision or imagination to help you do this project. As long as the extension is supported well you should be able to add to the desk. You might want to be sure that you can drop the extension when not in use. The piano hinges are a good choice for the weight. Make sure your legs are foldable so that you can put things away nicely. It is doable as long has you have the vision.

finally figured out adding photos
 

Sorry it took so long but here are the photos of my desk with the attachment.

Good Luck