Subbing Non-Fiction for Children

I'm putting together a few ideas for non-fiction books for children, but I'm at a little bit of a loss as to what to actually submit.

Because children's books are so much shorter I was wondering if I should sub the whole thing, but then if it wasn't polished (and I'm not sure if non-fiction should be polished due to normally subbing an idea) then, and I hate myself for saying this and sounding paranoid, could a publisher think, 'hey, we could get somebody else to write this ... only better.'

So, considering I don't really know what the 'polished,' version would need to be and I don't want my ideas nicking, should I just sub the outline, throw in a few facts and hope they ask to see more?

Sorry to be a Miss Fussybritches.

I've seen loads of people in the past ask the same question relating to fiction ideas and my attitude is that if somebody can write it better then so be it.
But with non-fiction the whole thing felt a little different particularly since a publisher would have a lot of input regarding the finished article.

Thanks though because I've stopped twittering now!