Is there a toy box mode for DS games?
I could not verify that you can use Ps1 toy box mode on Nintendo DS. Things you could try to answer your question. Go to the Http://nintendo.com site and look at the playing online information, game download information and the Toy Story 3 DS game.
I wish you luck in finding out if their is a toy box mode. From all I could research, no one claimed the Nintendo DS had a toy box mode. However, with a blank DS game card that is now available, a lot of games can be downloaded and saved on this blank card.
If the Ps1 toy box mode is available online or if you can upload it to a computer, you could try to download it to a DS. If you do not yet have the DS, ask to borrow someone's and carefully try what I have suggested.