No, in order for you to be logged into the game at the same time you both need to have separate SE accounts tied to separate PSN accounts, have purchased the game for both accounts and have two subscriptions for each. There is no way to transfer a character to a different SE account. This is standard for MMOs. If you are planning on rebuying the game and want to play together probably your best option is to tie that version of the game to a new SE account and its own PSN account and one of you starts a new character.