1851 census Ballameanagh, Jurby HO 107/2524 f9 p11 sch 37
Thomas Cavendish H m 33 Shoemaker b. Jurby
Ann Cavendish W m 33 Jurby
Ann Cavendish d 9 Scholar Jurby
Margaret Cavendish d 7 Scholar Jurby
Thomas Cavendish s 5 Scholar Jurby
John Cavendish s 3 Jurby
Robert Cavendish s 1 Jurby

I got the impression that whoever was writing up or copying the register omitted the father’s name by mistake, especially as it was the same as the child’s, perhaps confirmed by the fact that the words Ballymeanagh and shoemaker are consistent with siblings’ entries either side of Thomas’s.

All in Film 106725 (baptisms 1840-1871 St Patrick, Jurby) – – [MNHL May 05]:

1843, Aug 8th (No. 119) Jurby St Patrick,
Margaret, d. of Thos Cavendish, Ballameanagh, Shoemaker & Mary Ann Curphy, Jurby

1845, Sept 21st (No. 176) Jurby, St Patrick,
Thomas Cavendish, s. of Ann Curphey, Bally Meanagh, Shoemaker

1848, Feb 13th (No. 247) Jurby St Patrick,
John, s. of Thomas Cavendish, Sandygate, Shoemaker, & Ann Curphey

1852, May 16th Elizabeth, d. of Thomas Cavendish & Anne Curphey, Ballameanagh, Shoemaker

Thomas and Ann were married in 1839, as you suggested:

No.41 Jurby [MNHL Oct 04]
Thomas Cavendish, Bachelor of this Parish and Anne Curphey of this Parish, were married in this church by Licence this ninth day of November in the year 1839 by me, curate….
Thos. Cavendish X his mark
Anne Curphey late Cavendish her X mark
John Lane and Thomas Corlett [witnesses]

To my mind it is still not clear who the Barrow Thomas is, as the one in Douglas seems just as identifiable.