Battered women's shelters love to receive quilts. They would have children there. And lots of other suggestions you've already received.
I make my baby quilts about 45" x 54". There are a lot of baby panels that are 36" x 45". I think they're intended to be finished size, but I always add about a 5" border all around.
There are baby fabrics that can be cut into squares to make a quilt. Just random squares of a size you like would work. If you cut 6" squares, you'll get 9 squares out of a fat quarter. The squares will finish at 5.5", so a quilt 7 squares x 9 squares would be 38.5 x 49.5".
There are quilts that are just strips of baby fabric, alternated with another coordinating fabric or solid. Just make those the width of fabric, and the length that you want.
Then I was about to mention the one listed just above, but it's already there.