Oh the irony!!!
No charge!
No, "I doubt that" is not even a complete sentence because the word "that" introduces a subordinate clause which depends on the main clause to make a complete thought. To make it a complete sentence, you need to add a main clause after "that," such as in "I doubt that he will be on time".
Incomplete sentence: "I doubt that." (This leaves the listener wondering what is being doubted.)
Complete sentence: "I doubt that he will be on time." (The clause "he will be on time" completes the thought).
Oh the irony!!!!