Would you use USB or the cloud storage or what?
Or is it just DLC?

just try to download the dlcs from your account. But you can't use gameshared items.

This still hasn't been confirmed yet. But as Tom O' Connor mentioned that the levels are going to be transferred, there's a high possibility our profiles are also going to be transferred.
A USB could be the most accurate prediction on how to transfer your profile to the PS4. I don't think the whole cloud thing could work since not everyone has PSPlus.

you can test it with other games too.

The DLCs are not saved on the USB dive. they are bound to your PS system.
so you have no acces to the folder. You must have the DLC on your account to use them on another system.

Who knows, maybe the last update has introduced a secret system that upload your saves to the cloud.

It would be logical as the update is new and the beta comes soon. They have enough time to fix eventual bugs caused by this system, to have it ready for beta testers, and then LittleBIGPlanet3 players