I'm sure that 'a week today, a week tomorrow, a week on Monday, a week next Monday, a week this Monday, etc.' are correct expressions. They are British expressions and we do not need any punctuation marks as My Language Tutor said. (You can use Oxford Advanced Learner to check that the information is correct).
Also, I already know that the Americans use 'a week from today, a week from Monday, etc.). British people use these expressions too. Therefore, the omission of the preposition 'from' does not change the meaning as MLT said.