One thing that would concern me about the nails is rust, especially on a white blanket. I wonder too about sharp nails protruding from the wall as the child gets older and starts exploring, though maybe I am not seeing your plan the right way. The rack will not leave the blanket flush to the wall, and I am thinking the stitches in the blanket would stretch over the nails and come loose. Also, wood is definitely not acid free.
I am a picture framer and I have framed a number of crocheted pieces (though never one quite as large as this) so I will throw in my $.02 just to add to the confusion (sorry!). It will definitely preserve the piece better to have it framed, but it is very labor intensive and you would want to use high quality materials, both of which you will pay for.
As others have said, normally the piece would be sewn with either strong thread or monofilament (loosely, so you don’t tear the yarn fibers) to a piece of acid free mat (sometimes called “rag mat”). They also make a device similar to a switch gun, like the ones used in clothing stores to attach price tags, with those little plastic strips. I have no experience with these though, they may be too rough on the fibers. I am also not sure where you could buy one, other than a framing supplier (not cheap!).
I am thinking perhaps you could use a piece of rag mat or foam core (preferably acid free, but the regular kind is still much better than something like cardboard, which is loaded with acid and very bad for any kind of art). The rag mat is probably slightly better for the fiber and comes in more colors. The foam core is probably easier to work with, but usually only comes in black or white (acid free foam core is usually an ivory color, which would give a little contrast with the color of the blanket). Cut the board to fit a large ready-made frame, then either stitch, or if you must, tack the blanket to the mat board/foam core and fit it into the frame without the glass.
You definitely do not want glass resting directly on the fiber, the condensation that forms on glass will eventually rot the fabric. Plexiglass/acrylic is better against the art, but the quality stuff is expensive and I think it looks kind of ugly to have the crochet stitches smooshed up against it. One downside to doing it this way is that if the blanket gets dirty (since there is no glass, this is pretty much inevitable) and you want to clean it, getting it down and back up will be a bit of a production.
Ideally, you would do a shadowbox, or some kind of build-up in the frame to raise the glass and fit it with UV protective glass, but that gets trickier and more expensive. By doing it this way, you would at least have a little more flexibility, and spare your walls a few holes. And I think it will be a bit gentler on the blanket. If you have the piece all mounted, you may find a frame shop that is willing to work with your mounting and fit it into a shadowbox with UV glass for you. That would save you a lot of money, but the shadowboxes are still not cheap, and most ready-made frames are not deep enough to build one.
Standard mat board/foam core size is 32x40 inches, and should be easily available if you have a large art or craft store near you. You can also order from someplace like Dick Blick. Just figure on cutting it down to a standard frame size that will give you at least an inch or two all around the blanket (and remember, the blanket will stretch, I’d err larger, it will look better). You won’t be able to get a perfectly even border, especially working with a standard sized ready-made frame, but it is much cheaper than a custom frame. I think on a crocheted piece that size, you are going to get some sagging no matter what you do, but that doesn’t usually bother me, it isn’t supposed to look like a painting on canvas, it’s a blanket!
Just a few thoughts. Good luck with whatever you decide to do!