Define: "without any problem"
That is quite simple. When you disregard some of the spellings (like "hast" for "has", "doest" for "does") and accept the fact that when one person is addressed the KJV uses "thou", and when there are many it is "you" (like in German) what do you have?
Plain English (no hidden codes) as see here in John 1:
1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 The same was in the beginning with God. 3 All things were made by him; and without him was not any thing made that was made. 4 In him was life; and the life was the light of men. 5And the light shineth [shines] in darkness; and the darkness comprehended it not. Just one word that goes by the older spelling.
Of course a child would need the explanation for "comprehended". So would any adult.
Could a child read this and understand as in the KJV 2000?:
And the light shines in darkness; and the darkness overcame it not. But even "overcame" is not entirely correct. The meaning of katalambano is "to lay hold of" or "to seize" or "to capture". So here is where anyone would need to use proper Bible study tools. That should be SOP for anyone studying the Bible.