Betsey was definitely baptised at St Mary the Virgin, Hale.
Thomas married Alice Garnett at Childwall on 15 Apr 1805 (IGI, not seen the original yet).
Thomas & Alice's children, nearly all baptised at Hale:
27 Oct 1805 John the son of Thomas Dunbavan of Speke Labourer by Alice his wife was born Septbr. 21st and baptized October 27th 1805
(married Alice Madock at Childwall 22 Dec 1828, died at Oglet 08 Feb 1883)
10 Jan 1808 Thomas the son of Thomas Dunbavan of Oglet Fisherman by Alice his wife was born Decr. 19th 1807 and baptized Jany. 10th 1808
(married Ann Houghton at Hale 23 Apr 1832, died at Hale 18 May 1886)
27 May 1810 James the son of Thomas Dunbavan of Speke Labourer by Alice his wife was born May 3rd and baptized May 27th 1810
(no marriage traced, died at Oglet 15 Jan 1850).
11 Apr 1813 Betsey daur of Thomas & Alice Dunbavin, Speke, Labourer
27 Aug 1815 Ralph (IGI, not seen the original yet).
(married Alice (Houlgreave), widow of John Maddock, at Hale 28 Mar 1853)
1818 Henry (no baptism yet found)
(married Mary Southern at St. John's Old Haymarket 30 Mar 1845, died Oglet Dec 1902)
06 Aug 1820 William son of Thomas & Alice Dunbavin, Speak, Sailor
(married Mary White, Q3 1845 West Derby 20 957, died Garston Q2 1891 West Derby 8b 559).
03 Aug 1823 Alice daughter of Thomas & Alice Dunbavin, Speke, Salt labourer
(married Joseph Leadbetter at Childwall Q2 1842 West Derby 20 626)
31 Jul 1825 Mary daughter of Thomas & Alice Dunbavin, Oglet, Fisherman
(buried at Hale 06 Feb 1826)
04 Feb 1827 George son of Thomas & Alice Dunbavin, Oglet, Fisherman
(no other details found yet)
Records are from the Bishops' Transcripts at Chester (MF354/1) or at the LRO (DRL2/19).