Rather than reading your own speculation in to a passage which you assume will favour completely different religion, you should be honest enough to look at the context, and the rest of the theological analogy.
I agree with you, the Devil would know God pretty well, thus why ask the question and present the challenge: if you are the Son of God jump. Would it be because the Son of God himself understood his position? Otherwise the satanic challenge makes no sense.
Secondly, why should the devil doubt when God already had presented the facts: 'And a voice from heaven said, "This is my Son, whom I love; with him I am well pleased"'.
Thus, the issue is not that of doubt, nothing indicates that the devil is doubting, the concern is not even about the 'Son of God', the issue concerns temptation. Thus verses 1-3: 'Then Jesus was led by the Spirit into the desert to tempted by the devil... The tempter came and said...'