This USED to be one of the best sites for music, but it looks like the dreaded 'cuts' may have hit it. It used to show all possible instruments for children; I'll leave you to search it, and there may be a companion site, in the hope you can glean something from it:
Hi there are smaller basses these days (when I learnt in the 80s mini basses didn't really exist so I started on the one I still play straight away at age 13). I would say six is a bit little. Mainly because even on a small bass a lot of strength is required in the hands and fingers of the left hand. Much more than say a cello. The stretching is that much more. Do your local authority music service have a teacher who could advise? It's great to hear she has fallen in love with it. I love playing bass and it is a really cool instrument. As a teenager I got involved not only in orchestral playing but also jazz bands etc.