"It is a desk."
It depends how you added it. (And also that it would be more specific than the original sentence.)
Arguably, "It is a desk" and "It is one desk" mean roughly the same thing, 一つのつくえです could be acceptable when you're translating from English to Japanese, but because Japanese doesn't differentiate between plural and singular, when translating つくえです to English, it can mean "It is a desk" or "they are desks". Perhaps it's an oversight on the part of the course developers to disallow 一つ because it's not a symmetric translation.
However, つくえの一つです means "It is one of the desks", つくえが一つです means "There is one desk", 一つがつくえです means "One (of the things) is a desk", etc. No other combinations I can think of work for it to mean "It is one desk".
机はです is grammatically incorrect*. です is a special kind of verb, especially in such short sentences.
If you think of the general SVO sentence "A is B", where A is the subject (in English) and B is the object (in English), you would have to write it as AはBです in Japanese. If it's obvious from the context what A (the topic) is, you can leave it (and は) out, but if you remove B (the object), you have an incomplete sentence - "A is ..." what?
*Side note: you can leave out B too if it's very obvious from the context, but it's uncommon and this basically only happens if someone is asking you to reconfirm the topic and/or you want to prevent repeated misunderstanding of the topic.