The Special Relativity Theory won't help much, the disassemble and re-assemble on the atomic level is the problem. Actually, it is quite impossible. It is a dead-duck situation...

There is no fundamental difficulty in teleporting large objects. If I want to teleport an object, say a doll's house, to Alpha Centauri, I send a construction manual by radio beam, and on Alpha Centauri the doll house is built up out of local materials. The only difficulties are technical. Or maybe I do not get the question right?

Yes in theory, no in practice. I think there is a misunderstanding of how teleportation works. In quantum teleportation, there are 2 key elements:

(1) In teleporting from point A to point B, you need a local quantum system at point B already there. The quantum system at point A does not vanish from A and reappears at B but only its information (quantum state) is teleported from A to B.

(2) classical information (which cannot travel faster than the speed of light) is required to complete the teleportation. As such teleportation obeys special theory of relativity.

If you teleport a person from point A to B you effectively kill the person a point A to extract ALL its information about each and every atom, and using this information you reconstitute an exact replica of the person using the local atoms at point B.

Here is how Charles Bennett (the discoverer of teleportation) humorously explains explains teleportation (reconstructed from memory).

There are two twins, Romulus and Remus, who have a special bond [entangled pair]. When asked a question they give a random answer, but they both give the same answer:

Teacher: What is the color of the grass?

Romulus: Pink mam.

Another Teacher in a different room: What is the color of the grass?

Remus: Pink mam.

Then a crime is committed in Boston, and there was a sole eye witness [quantum state to teleport]. FBI in Washington DC wants to investigate, but the the witness in Boston is very forgetful and if they attempt to fly him in to DC, he wold have forgotten everything under the stress of the murder [quantum states are brittle]. Also, they have no qualified person in Boston to interview the witness (and they don't trust the local police either). Fortunately for them, Romulus in in Boston and Remus in Washington DC. So they ask Romulus to spend time with the witness to talk about anything they want: weather, baseball game, latest movies...

After about an hour spent chitchatting with Romulus the witness leaves the room, stating that he haves Romulus, and he dislikes everything Romulus likes, and he hates whatever Romulus likes [classical information to be set from point A to point B]. Moreover, the stress of the meeting has forever erased the memory about the murder [quantum states are destroyed when measured].

So can FBI teleport the information about the murder from Boston to Washington DC? The original information seems to be destroyed, but is it? FBI can now asks Remus about the murder (which he did not witness, an apparently he will give random answers), and using the fact that Romulus and Remus are correlated, and Romulus is anti-correlated with the witness, they reverse every yes-no answer from Remus and find out all information about the crime. Teleportation was successfully achieved.

I see. But this seems to be teleportation of classical information (about the murder),

not large objects. And in this case: why not use a telephone line to interrogate the witness? I do not want to spoil the story, but I wonder if it is related to the question.

" why not use a telephone line to interrogate the witness?"

Because in this case it is not teleporting, but pure transmission of classical information. The story has to be taken with a grain of salt, because it is about macroscopic objects.

The problem in quantum world is a theorem which states that information cannot be duplicated (unlike in the classical realm) because this breaks unitarity. The teleporting protocol works like this:

start with an entangled pair and the quantum state to be teleported. Combine one of the pair with the source and perform a measurement. This destroys the original quantum state, but generates an outcome which can be used as a key. Transmit this key (classical bit of information) to the remote location of the second pair, and based on the key perform one of several types of measurements (you pick a particular basis for measurement). The second measurement creates a copy of the original quantum state. In the process the original quantum state is destroyed, and the no-cloning theorem is obeyed.

So instead of carrying the original quantum state from point A to point B you carry a classical bit of information which allows you to recreate the quantum state at point B.