I believe the only way you'd be able to download an already purchased game from the eShop would be to do a system transfer to your new 3DS, which moves over all your settings and Nintendo ID information to your new console. The only problem with that is you can no longer use that account on your original 3DS. I'm also not sure if you lose access to your downloads once you do this as I've never tried it myself, but I'll let someone else answer that if they've done a system transfer.