I used to get the paper bags (don't know if they even have these anymore, they used to be two bags with a head hole in the middle that you would wear) and hang them from my handlebars as a kid, this way I could throw the papers without stopping.

Make sure the paper collects the money for your daughter though. Sending the kids out to collect the money is a seriously very bad, risky, stupid idea. I don't think papers do this anymore but I have to warn you if they do still make the kids collect the money for them you may want to accompany your child when they go to collect. Had a very bad experience when I was 10, wouldn't wish it on my worst enemy.

Regarding a trailer, it might be easier to find a used burlery or something like that. I think Walmart or Costco sells trailers but I wouldn't expect them to last very long. I have heard good things about REI's trailers though. I contemplated making a trailer out of PVC pipe once, but didn't get to far past the concept stage.