Save your toyboxs to the cloud on PS3 and redownload them onto the PS4.
That's about the only thing you can save.
I did do this, but I discovered that I in order to edit certain features of the ported toy boxes, I had to erase and recreate whatever I was editing.
For example, I had put the replayer in plain sight on the PS3, but it wouldn't let me select it to move it out of sight, so the logic connection had to be rebuilt from scratch.
The same applied to anything I created in the PS3 version, it was unselectable.
If you own the figures and they are marked as owned, then you get to keep the levels.