Should I use [sic] when quoting the KJV 1611?

I should say that littering a text with "[sic]" is unhelpful. If it's obvious what you're quoting, then you're quoting it.

You might cite it as "(Col 4:1, KJV 1611 as printed)" or something.

Certain letters might cause technical difficulties, like yͤ. Bear in mind also that this is a transliteration, and probably incorrect. Although your text has giue because the blackletter v looks very much like the modern u, complete with a tail, the correct transliteration into modern Roman type as you have here is arguably v, because that's the letter which produces the sound the blackletter character did. It's a similar problem with transliterating Cyrillic: is Романовы "Pomahobbi", "Romanov", "Romanev" or "Romanoff"?

If your text had Roman characters, then it would be reasonable to copy those.

You might be interested in the King James Bible website — there is an edition of 1833 which does the Romanisation you want [and could therefore simply be copied verbatim, but is 1833 not 1611]; but note how the 1611 title page spells out, tongues and Churches; the blackletter text for those words would probably not use the look-alike 𝖚. However, revised does use a u as well as a long s. Transliteration is not straightforward. If you're going to do it, spend time to get it right. Don't get it wrong and annoy your teacher.