I don't have any experience of the double bass, but one of my children plays the cello. I'd have thought the double bass was a good option - there are unlikely to be masses of other players, which will help get her into orchestras. It will also give your daughter the ability to play in a jazz type group as well as a traditional orchestra, which she might enjoy when she is older.
You are obviously considering other instruments, though I'm not sure if you are considering them as an addition or alternative to the double bass. If she has no motivation to practise the double bass, will she be any more motivated to practise another instrument? Playing any instrument well is hard and takes hard work. I think lots of children can get to a certain level reasonably easily but then get stuck and can't make more progress without increasing their efforts substantially.
I don't have any experience of any wind or brass instruments, but my understanding is that, at the early stages, the clarinet, flute and trumpet are probably the easiest instruments to make quick progress on (plus the saxophone). If she wants a loud instrument, the trumpet or clarinet would be the best, and would also give her more options over genre.
A few questions to think about: 1) Whose choice was the double bass? Hers or yours? 2) Does her teacher think she is making good progress? Your daughter might just need reassurance about that. 3) does her school or music education hub offer any opportunities for children to try out various instruments? 4) what is music like at her primary school? Do they offer whole class instrumental teaching for some year groups? If so, is it in an instrument she's interested in (in which case you might as well just wait until she starts at school. 5) will it be easy to find a teacher in the chosen instrument in your local area?