I’m going to suggest a very different approach. Rather than get a “real” backpack below a pound, how about a UL daypack below 3 ounces?
Stuffed animals, a quilt and sleeping pad aren’t a #10 can of peaches (I’ve put those in kids’ packs in 1970s). They are soft, low-density and often the biggest benefit of what the child carries is its VOLUME not its weight, since the adult’s pack is short of volume.
What I’ve used on our kids until they are 70-80 pounds is a light-weight sil-nylon daypack. 2.7 or 3.2 ounces, they hold about 18 liters. No padding, no hip belt, minimal shoulder straps, but all of that is fine with 4 or 5 pounds in it. Here’s Sea to Summit’s 20-liter 2.4-ounce version:

$32.95 at REI or $21.95 + $3.45 postage at: www.trekkinn.com
I can vouch for the fit and usefulness of the Sea-to-Summit one. I’ve also had good luck with some cheaper options out of China on eBay. Can’t find them now, but I got some supposedly “Bear Grylls” 18-liter, sil-nylon, highly packable day packs for $11 each. Searching eBay today, I see some tempting 35-liter versions for $9 + $3 shipping out of China, but they give no weight on it.
Okay, so you don’t get a UL backpack for you to use, but you do get a UL daypack for you to use 1) as over-flow volume such as after a food resupply on a thru hike or for a few longer waterless stretches – wear it on your chest in those cases, 2) as a multiple purpose item in your larger pack as a stuff sack and as a day pack for side trips, 3) when traveling, should there be “mission creep” and you need more luggage capacity on your way home, 4) when around town, it fits in your pocket on the way out but helps haul your groceries on bus/bike ride home.