I think it's normal.
Ds has a crocheted blankie that belonged to dh when he was a baby. We do not leave the house without the blankie. Period. We went to the park last week and he wanted to run around carrying it. Once I tried to run in and out of the post office with him and left the blankie in the car and he was almost hyseterical in the 30 seconds it took for me to check the post office box. Also in his crib he keeps another crocheted blanket, a book a teddy bear, the sleeve from the "Meet Joe" video and my pajama pants. I left the pants at the foot of my bed, where his crib is, and he dragged them in. I took them out and put them back and I just left them. Today I washed his bedding, including the crocheted crib blanket. He likes to "help" me load the dryer and he saw that blanket going in and ran off with it! It was only damp so I let him play with it and dh stuffed it in the dryer while I gave him a bath. Oh and washing "blankie?" Forget about it! I have to stuff it under my shirt to get it to the machine. Usually I just wait until I take him to MILs and have her wash it while he is busy playing with his aunts.