Yes, that's normal. I got my Betty Boop when she was 12 weeks old and for quite a while she slept with her head between my chin and shoulder blade each night. It made her feel secure. As she grew older, she moved down a little bit and we began to spoon! She is now about 10 months old and she starts out with her head on my pillow, she turns around and kisses me, and then moves to my tummy and we spoon all night!
I just love this! She is a sleepy head and sleeps all night. During the day, she makes every step I do. However, where she once stayed in my lap a lot, she no longer does this because she is more curious now. We play fetch a lot. I miss her sitting in my lap like she used to.