If I don't have the Dawnguard DLC, can I still get Serana as a follower?

As a previous commenter said, the real question is why won't your PS3 allow you to download it? There were issues previously with getting Dawnguard to work with PS3, but these were fixed back in 2013. Maybe your drive doesn't have enough space?

Serana is not inside Fort Dawnguard. According to UESP she is in a coffin inside Dimhollow Cavern, which is a location specifically added after installing the Dawnguard expansion. So without Dawnguard, you won't be able to get her. Since you are playing on PS3 you can't use any console hacks to add her either [I don't even know if this is possible].

Dawnguard was previously unavailable for PS3 but it can now be purchased from the store. If that doesn't work for some reason and you are really desperate for her, you can download the Special Edition which already has all three DLCs included, but this would mean buying another version of the game with the possibility of starting all over again.

If I were you, I'd look more into why you can't install Dawnguard or choose another follower. It sounds like a local issue and something which is technically related rather than something specific to the game.