LittleBigPlanet DLC Redownload issue...

I recently just sold my PS3, because i'm upgrading to a PS4 soon. Luckily, I know my PSN credentials.

But there's one problem. I have DLC downloaded specifically for LittleBigPlanet, and I want to move the downloads to PS4. I have downloaded them many times in the past, and I never had an issue finding out how to do it.

Can you, or can you not redownload DLC you purchased on PS3, to PS4? I need to know before my LBP DLC is gone forever.

I know 1 and 2 are not on PS4 yet, but you can still use the DLC in LBP 3 which is on PS4. I need to know before I download my DLC back. (NOTE: It was Free DLC)