When my daughter was that age she was very close to my mother as I was always working...
So what I did to bring us closer together, is set aside time for activities that she particularly liked, and actively joined in on them, not just supervise.
Much to my dismay one of the things she absolutely loved, was playing dolls!
So former tomboy turned single mommy sheepishly asked her lil girl to teach her how to play.
She was overjoyed that she could actually teach me something, and beamed at the fact that I took an interest in something she did, and in return, I let her join me with something I did.
So I would paint her nails for her when I painted mine, and even allowed her to paint mine when she asked.
I know I know, make up and little girls can be a hot topic, but it was only nail polish, no facial products, and the gamble MORE than paid off because these days we are as thick as thieves.
She's 10 now btw...