I wonder where he qualified and whether he is in any Navy Lists?

A few Naval Lists have been examined but none are clearly identifiable as him.

However this site does seem to have a usable list <http://www.pdavis.nl/Surgeons_1840.htm>;, from a combination of the January 1840 Navy List: Medical Officers with the Dates of their Seniority; Alphabetical List of Medical Officers; and List of [the ships of] the Royal Navy, with their Present Positions.:

Surname  Christian name(s)  Seniority  Ship  Station

Surgeons

Smith George  09.02.1810     half-pay
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In 1841 they were living on the High Stree at Moffat, Dumfires; he was a Naval Surgeon HP (on half-pay) and they had with them these children:

Forename     Age    Birth

Esther        20    Dumfriesshire, Scotland
Elizabeth     15    do
Jane          12    do
Samuel        10    do
James          8    do
George         6    do
Mary           4    do
Edward         1    do

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In 1851 they were living in Moffat, he was a Surgeon RN, unfit for sea but acting as a General Practitioner, in a large establishment with a daughter and her family and a partner doctor.  The children were:

Forename  Surname     Relation  Cond  M/F Age   Occupation   Birth

Mary      Smith       Dau       Unm    F   13   Scholar      Moffat, Dumfries
Edward    do          Son       Unm    M   10   Scholar      Moffat, Dumfries
Maxwell   do          do        Unm    M    8   Scholar      Moffat, Dumfries
Esther    Bloomfield  Dau       M      F   33                Moffat, Dumfries
George    do          Grandson         M    2                Moffat, Dumfries
Robert    do          do               M    1                Moffat, Dumfries
(unnamed) do          do               M    1m               Moffat, Dumfries

They had a nurse, three serveants and a stable boy to help look after them all.
The partner was James Munro MD of Edin burgh University, LRCS.
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In 1861 they were living at Vicarland Terrace on the High Street, Moffat; he had retired as a GP but was still listed as a Surgeon RN half pay Not in Practice.  They had two servants attending on them.  All children had left.
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His death was certified on the 5th June 1861 and the certificate says:

He was a surgeon in RN, and dies at 10 AM (?) on 3 June, at Vicarland, Moffat aged 73
His father was William Smith a farmer, deceased.
His mother was [illegible] Smith née Cowan (?), deceased.
He died of Paralysis for 20 months, certified by James Munro MD.
The informant was also James Munro MD, son-in-law who was present at the death.
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The death led to his birth record, on the baptism register as:

George son to William Smith and Jean Cowan Spouses in Marriage was born on the 24th of Aug and baptised on the 2nd of Sept.

This very clearly gives his mother’s name.
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Here are all the Smith births in Moffat whose mother was Esther White:

    Bapt                       Parent Names                 City   GROS
No  Date  Surname  Forename      Frame No.   Sex  Parish   County   Data
1 27/06/1840 SMITH EDWARD STACE GEORGE SMITH/ESTHER WHITE FR1190 M MOFFAT /DUMFRIES 842/00 0050 0083
2 21/05/1819 SMITH ELISABETH GEORGE SMITH/ESTHER WHITE FR299 F MOFFAT /DUMFRIES 842/00 0010 0384
3 02/10/1822 SMITH ELISABETH GEORGE SMITH/ESTHER WHITE FR1120 F MOFFAT /DUMFRIES 842/00 0050 0015
4 26/06/1816 SMITH GEORGE GEORGE SMITH/ESTHER WHITE FR129 M LOCHMABEN /DUMFRIES 840/00 0010 0237
5 03/09/1835 SMITH GEORGE GEORGE SMITH/ESTHER WHITE FR1173 M MOFFAT /DUMFRIES 842/00 0050 0066
6 25/09/1824 SMITH JAMES GEORGE SMITH/ESTHER WHITE FR1128 M MOFFAT /DUMFRIES 842/00 0050 0023
7 30/12/1828 SMITH JANE GEORGE SMITH/ESTHER WHITE FR1146 F MOFFAT /DUMFRIES 842/00 0050 0041
8 22/02/1826 SMITH JOHN HALL GEORGE SMITH/ESTHER WHITE FR1134 M MOFFAT /DUMFRIES 842/00 0050 0029
9 15/05/1837 SMITH MARY SYMONDS GEORGE SMITH/ESTHER WHITE FR1179 F MOFFAT /DUMFRIES 842/00 0050 0072
10 17/09/1842 SMITH MAXWELL GEORGE SMITH/ESTHER WHITE FR1202 M MOFFAT /DUMFRIES 842/00 0050 0093
11 25/02/1821 SMITH S WILLIAM GEORGE SMITH/ESTHER WHITE FR1113 M MOFFAT /DUMFRIES 842/00 0050 0008
12 24/11/1830 SMITH SAMUEL SYMONDS GEORGE SMITH/ESTHER WHITE FR1156 M MOFFAT /DUMFRIES 842/00 0050 0050
13 04/02/1820 SMITH WILLIAM GEORGE SMITH/ESTHER WHITE FR1110 M MOFFAT /DUMFRIES 842/00 0050 0005
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The above 13 children in order of baptism dates:

George,         bpt 26 Jun 1816
Elisabeth,      bpt 21 May 1819
William,        bpt 04 Feb 1820
S William,      bpt 25 Feb 1821
Elizabeth,      bpt 02 Oct 1822
James,          bpt 25 Sep 1824
John Hall,      bpt 22 Feb 1826
Jane,           bpt 30 Dec 1828
Samuel Symonds, bpt 24 Nov 1830
George,         bpt 03 Sep 1835
Mary Symonds    bpt 15 May 1837
Edward Stace    bpt 27 Jun 1840
Maxwell,        bpt 17 Sep 1842
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This looks like their marriage registry abstract:

Name:             Esther White
Gender:           Female
Marriage Date:    10 Oct 1815
Marriage Place:   Alverstoke,Hampshire,England
Spouse:           George Smith
FHL Film Number:  918903

I need to get hold of a copy of the register entry.
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