Your really old tarnished small brass doorplate - Captain’s Office -SS Titanic is more than likely a fake! - Sorry!
The Titanic sunk in the North Atlantic on 15th April 2012 with a loss of over 1500 lives. From that day on the Titanic has captured the imagination of millions. How could the ‘unsinkable’ White Star liner- the most luxurious of its day - go down so quickly (only 2 hrs and 40 minutes!)?
Since The wreck was discovered in 1985 there has been an enormous interest in anything associated with the Titanic. Artefacts brought up from the wreck - wallets, plates, toilet keys, shoes, coins - absolutley anything is worth a lot of money. A china saucer fetched $20,000 at auction and even a rivet (yes a rivet!) sold for $15,000!!
Your brass doorplate reads SS Titanic. The correct designation should be RMS (Royal Mail Ship) Titanic. The most likely thing is that it was made as a souvenir following the sinking, maybe in the early 1920s?
Someone asked a fairly similar question on Blurtit. Have a look at the answers here
But - you can never really be sure until you have a valuation. Get some proper advice. Have a look at this video which looks at Titanic memorabilia & artefacts. Good luck!