I put "Ca c'est ma nouvelle robe noire".. that should be accepted!
No it can't because what you wrote would be "that it is my new, black dress", which is not correct in English either.
The demonstrative notion is included in c'= ce (this/that/it)
What's the difference between nouvelle and nouveau? (merci)
nouvelle is feminine and and nouveau is masculin
What's your thought on"Celui ma nouvelle robe noire"
No, it does not work, notably because you have skipped the verb.
"this is" = "c'est" or "ceci est"
"celui" = the one