Here's the Ballad index info:

Over the Water to Charlie
DESCRIPTION: "Come boat me o'er, come row me o'er, Come boat me o'er to Charlie." "We'll o'er the water, we'll o'er the sea, We'll o'er the water to Charlie." The singer tells her love for Charlie, laments his exile, says she would bear her sons again to die for him
AUTHOR: Robert Burns?
EARLIEST DATE: 1788 (Scots Musical Museum #187)
KEYWORDS: love Jacobites separation exile ship
HISTORICAL REFERENCES:
1720-1788 - Life of Charles Edward Stuart, "Bonnie Prince Charlie"
1745-1746 - '45 Jacobite rebellion led by Bonnie Prince Charlie
Apr 16, 1746 - Battle of Culloden. The Jacobite rebellion is crushed, most of the Highlanders slain, and Charlie forced to flee for his life.
Jun 28-29, 1746 - Aided by Flora MacDonald, and dressed as her maidservant, Charles flees from North Uist to Skye in the Hebrides.
Sep 20, 1746 - Charles finally escapes to France
FOUND IN: US(NE)
REFERENCES (2 citations):
Linscott, pp. 262-263, "Over the Water to Charlie" (1 short text, 1 tune, with one verse of this and two of the "Charlie" verses of "Weevily Wheat")
DT CHARLOVER* CHARLOV2*
Roud #729
Notes: Roud lumps this (and several other Bonnie Prince Charlie songs) with the "Weevily Wheat" family. Certainly Linscott's version is really just a "Weevily Wheat" variant which has swallowed a fragment of this song. But "Weevily Wheat" is a dancetune that mentions "Charlie" (not necessarily Charles Edward Stuart) incidentally, while this is a sure Jacobite song. As such, I separate them.
Just how much this piece owes to Burns is unknown to me; he surely had a hand in it, but it's interesting to note that there is a verse out there which he did not publish. - RBW