It sounds like you want to try hand piecing to see if you can do it and to see how it differs from machine work.
It also sounds like your little one really really wants a blanky of her own. Why not whip one out on the machine for her? She won't have a clue what "hand-made" means at her age. She will love whatever you make.
Your idea of making the hand-sewn project something without pressure is a wonderful one. I have a hand-prep project in the works that uses up scraps and I get to it when I have time. (I also have about 15 other WIPs going on - some with deadlines.)
You may be a newbie, but you are speaking the language of a true quilter.
Have fun.