I hardly like to do this, because it involves quoting wholesale from somebody else's site, but there's a good reason why this tune isn't easy to find as "O'Carolan's Dream". Here is the relevant stuff, copied and pasted as is, from The Fiddler's Companion:
BRIAN THE BRAVE [1]. AKA and see "Poll/Moll/Paul Ha'Penny," "Boys of Ballysimon," "Carolan's Dream," "Garrai Na Bhfeileoig," "Hawke's Hornpipe," "Molly Mac Alpin," "O'Carolan's Farewell to Music," "Remember the Glories of Brian the Brave," "The Stranger." Irish, Hornpipe. A Aeolian. Standard. AABB. Roche Collection, 1982; Vol. II, pg. 11, #212. Claddagh CC27, Michael Tubridy - "The Eagle's Whistle."
CAROLAN'S DREAM. Irish, Piece. A Minor. Standard. AAB. The tune is attributed to blind Irish harper Turlough O'Carolan (1670-1738), though Donal O'Sullivan, in his definitive work on the bard could find no incontrovertable evidence of its origin. Complete Collection of Carolan's Irish Tunes, 1984; No. 187, pg. 129.
GARRAÕ NA bhSILEIG (The Honeysuckle Garden). AKA and see "The Boys of Ballysimon," "Brian the Brave," "Carolan's Dream," "Hawke's Hornpipe," "Molly McAlpin," "Molly Mac Alpin," "O'Carolan's Farewell to Music," "Poll Halfpenny," "Remember the Glories of Brian the Brave," "The Stranger." Irish, Hornpipe. Bobby Casey - "Taking Flight." Gael Linn CEF 114, Noel Hill & Tony MacMahon - "Õ gCnoc na GraÌ." Shanachie 79006, Mary Bergin - "Feadoga Stain."
T:Poll Ha'Penny
T:Paul Halfpenny
T:Garra\'i na bhF\'eile\'og
R:hornpipe
Z:id:hn-hornpipe-26
M:C|
K:Amix
(3GAB|=cAAG A2 (3AB=c|(3d=cB (3AGF G2 (3B^cd|ed^cA d^cAG|~A3G A2de|
~f3d ~e3c|d2 (3Bcd efge|aged (3=cBA GB|~A3G A2:|
|:ef|~g3f gfef|g2ga gedg|eaag ~a3g|eaag a2ag|
~f3d ~e3c|d2 (3Bcd efge|aged (3=cBA GB|~A3G A2:|
"Version 2:"
AB|=cAAG A2GA|dcAF G2 (3Bcd|edcA dcAG|A2 (3AAA A2ag|
~f3d efec|d2 (3Bcd efge|agfd =cAGE|A2AG A2:|
|:ef|gfga gedB|=cdef gafg|e2a2 abag|e2a2 abag|
~f3d efec|d2 (3Bcd efge|agfd =cAGE|A2AG A2:|
MOLL HALFPENNY/HA'PENNY. AKA and see "Molly MacAlpin," "Paul/Poll Ha'penny," "Maili Nic Ailpin," "O'Carolan's Farewell to Music," "Carolan's Dream," "(Remember the Glories of) Brian the Brave." Irish, Air (4/4 time). A Minor/A Dorian. Standard. AB. "This name is the same as 'Molly MacAlpin,' and the air is a dance setting, and also a song setting--a very good one too--of the fine air (Molly MacAlpin) to which Moore wrote his song, 'Remember the glories of Brian the Brave'" (Joyce). Joyce, 1909; No. 134, pgs. 68-69. Green Linnett GLCD 1181, Martin Hayes & Dennis Cahill - "The Lonesome Touch" (1997).
POLL HA'PENNY (Maire Na Leat-Pingin/Pingean). AKA and see "The Boys of Ballysimon," "Brian the Brave," "Carolan's Dream," "GarraÌ na BhfÈileÛig," "Holey Ha'Penny," "Molly Ha'penny," "Molly Mac Alpin," "O'Carolan's Farewell to Music," "Paul Ha'Penny," "Remember the Glories of Brian the Brave," "The Stranger Hornpipe." Irish, Hornpipe, Long or Set Dance (4/4 time). A Mixolydian (Mitchell) or Dorian (Mulvihill). Standard. AB (O'Neill/1915 & 1001): AAB (O'Neill/1850): AABB (Mitchell, Mulvihill, O'Neill/Krassen). The dance version of the air "Molly MacAlpin," by the ancient harper Laurnce O'Connellan, born at Cloonmahon, County Sligo, in the mid-17th century (c. 1645). Donal O'Sullivan in his Carolan biography (vol. 1, p. 18) reported that the Irish harper and composer O'Carolan (1670-1738) thought so highly of this tune that he was supposed to have said he would rather have been its composer than any of his own melodies. Ciaran Carson (1996) remarks that the title Source for notated version: piper Willie Clancy (1918-1973, Miltown Malbay, west Clare) [Mitchell]. Mitchell, 1993; No. 99, pg. 86 (appears as "Poll Halpenny"). Mulvihill, 1986; No. 7, pg. 120 (appears as "Pol Ha'penny"). O'Neill (1915 ed.), 1987; No. 397, pg. 190. O'Neill (Krassen), 1976; pg. 208. O'Neill (1850), 1979; No. 1783, pg. 333.
O'Neill (1001), 1986; No. 983, pg. 169. Mulligan MUL 027, Martin O'Connor - "A Connaughtman's Rambles."
T:Poll Ha'Penny
T:Paul Halfpenny
T:Garra\'i na bhF\'eile\'og
R:hornpipe
H:The Irish title means "The Garden of Honeysuckles"
D:Mary Bergin: Feadoga Stain
D:Noel Hill agus Tony McMahon: I gCnoc na Grai
Z:id:hn-hornpipe-26
M:C|
K:Amix
(3GAB|=cAAG A2 (3AB=c|(3d=cB (3AGF G2 (3B^cd|ed^cA d^cAG|~A3G A2de|
~f3d ~e3c|d2 (3Bcd efge|aged (3=cBA GB|~A3G A2:|
|:ef|~g3f gfef|g2ga gedg|eaag ~a3g|eaag a2ag|
~f3d ~e3c|d2 (3Bcd efge|aged (3=cBA GB|~A3G A2:|
"Version 2:"
AB|=cAAG A2GA|dcAF G2 (3Bcd|edcA dcAG|A2 (3AAA A2ag|
~f3d efec|d2 (3Bcd efge|agfd =cAGE|A2AG A2:|
|:ef|gfga gedB|=cdef gafg|e2a2 abag|e2a2 abag|
~f3d efec|d2 (3Bcd efge|agfd =cAGE|A2AG A2:|
The Fiddlers' Companion is the place to go if JC's doesn't get you what you're looking for. There are no tunes there, but there is a great deal of information that will help you in your search.
Malcolm