My LGs are quite a bit younger than yours, but
1) detangling spray works wonders for us
2) My almost-5 year old can pull her hair into a loose ponytail or use a headband or barrettes, and she's getting good at brushing it. And her motor skills aren't that great, so I do think it's doable. I'm teaching her to pull the length over her shoulder to reach the ends. She hasn't had her first haircut yet, since she spent the first two years of her life being called a boy, even though now the longest part of her hair does reach the middle of her back.
3) A slightly longer version of the bob you posted is QUITE popular among young girls of all ages in my area, so I don't think you'd have to worry about her getting made fun of.
4) But your LG's hair is so thick, I'd want to make sure it would lay like that. I already told my oldest that she could cut her hair like a friend, but her thick curly hair would never look the same as her friend's thinner and very straight hair.
If you choose to get her hair cut, I'd definitely get input from her and a hairdresser. I too had a HORRIBLE haircut at 8 years old, forced because another child cut a chunk out of my hair. Not fun, not pretty.