You're quite correct. The ending -ㄴ 다고 is used when quoting what sb(including yourself) has said or written.
(verb + ㄴ 다고, noun + (이)라고)
사랑하다
사랑한다
사랑한다고
사랑한다고 말했다/했다/썼다, etc.
However, here it conveys stronger sense than just "사랑해".
"널 사랑한다고" without such endings 말했다/했다 is used when sb is full of emotion, and there are chances that sb shouted this phrase while crying(like on soap operas^^/)
(sb = somebody)
Here is another example,
A : 오빠, 사랑해(whispering) = Oppa, I love you.
B : 뭐라고? = What did you say?
A : 사랑해(whispering again)
B : 뭐? = what?
A : 널 사랑한다고, idiot! (^^/) = I said "I love you", idiot!!
\^o^/