Hope I didn't find this too late for you
I don't really know much about a Day 1 model (I'm sure it's as self-explanatory as it sounds), but I think all content (DLC and whatnot) are linked to your PSN account, not your console. Of course you'd have to redownload everything for your new PS4, but you wouldn't need to buy it all again. Though strange as it sounds, I have two PSN accounts on my PS4 (ones for soloing), and every bit of DLC I've got was bought on my main, though I can use it on my other account. I don't need two seperate PS+ subscriptions either...this leads me to believe that DLC is tied to your PSN, and accounts are tied to your console once you've set one as your primary system, allowing you to share between accounts on a certain console.
So yeah, in short your content is saved on your console's HD, but tied to your PSN account. You'd have to sign into your PSN on your old console, deactivate that console as your primary one for that account, sign into your PSN on your new console, set it as your new primary console, restore licenses(?), then redownload all your stuff again. You won't need to pay again though if someone could confirm those steps that would be great. I've only ever had one PS4