Is it valid to say 'I'm incredulous." all by itself as a standalone sentence? The intent is to convey that I am in disbelief. Thanks.
It's normally used when speaking with regard to someone else. The subject is also normally included. - 'He was incredulous at the news.'
Speaking about yourself with no subject, except the implied context in which the phrase is stated, you might use "skeptical" - 'I'm skeptical.'
Yes it is valid to say, 'I'm incredulous.', though you may want to include the subject about which you're incredulous, if it hasn't been implied by the context of the conversation or writing. Not doing so can be interpreted as being "stuffy or stuck up, thumb your nose up at...".
"I am x" or "I'm x" is a full sentence, with subject and verb, as long as x is an adjective.
Incredulous is an adjective, so this is a valid sentence.
It doesn't say much, and as Electric says, it's usually used to describe something you are incredulous about. But it is valid.