I'm a Division Commissioner and Brownie leader
Please don't force her, it is meant to be fun.
Could you try a different pack? They can be very different, I'm involved in two Brownie packs, very different atmospheres.
As someone said, Brownies will still be there in a year or so, and maybe even wait until she is Guide age, or we even had a girl join at 15, straight into Seniors having missed Brownies and Guides altogether.
Also if she is only just 7, those bigger Brownies (9-10+) must look enormous and scary to her, so she might be better next year when she's not the littlest.
I agree if she likes animals, maybe look into riding.
My dd was very anti-social, had speech delay and was tested, but not diagnosed, for Aspergers, having difficulties at school having had to change schools at the end of Y1, HATED Rainbows. She didn't like the leaders, didn't like the crafts, didn't like the running around screaming (it wasn't the best unit TBF).
At 8 1/2, we gave it another go and she joined Brownies and LOVED it, it was her thing completely and it was very good for her socially.
She's now 17 and a Young leader at Brownies, the leaders say its like having a 17 year old Brownie, and she spends most of the meetings with Brownies hanging off her and joining in the games.