Given the age difference between Dennis and Jane, we would immediately suspect he had an earlier marriage.  The children with him in the 1800 census support this view.

— born in Mason Co., KY:
  4.  Nathaniel CARRICO, b. 7 Jan 1805
  5.  Elizabeth CARRICO, b. 14 Sep 1808
  6.  Tabitha CARRICO, b. 20 Jun 1810
  7.  Reuben CARRICO, b. 1812

— born in MO:
  8.  (Daughter C) CARRICO, b. 1810-15
  9.  (Daughter D) CARRICO, b. 1810-15
10.  James B. CARRICO, b. 1816/7
11.  John Clark CARRICO, b. 28 Feb 1819
12.  Dennis H. CARRICO, b. 20 May 1821

— born in MO or Greene Co., IL:
13.  (Daughter E) CARRICO, b. 1822

— born in Greene Co., IL:
14.  Thomas C. CARRICO, b. 21 Dec 1825

1.  St. Louis Genealogical Society.  1999.  St. Louis Marriage Index, 1804-76. St. Louis, MO (online at Ancestry.com):

Dennis Carrico

Amy, Mrs James

9 Jun 1846

Vol. 3, p. 276

2.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

Dennis Carrico Birth: 26 Oct 1778, Bryantown, Charles, Maryland Death: 23 May 1852, Saint Louis, St Louis, Missouri Marriage: 09 Jun 1845, St Louis, Missouri Spouse: Amy Jamison Birth: 31 Oct 1790, Madison, Kentucky Death: 11 Nov 1865, Greene, Illinois Source: patron submission

Phineas JAMES Birth: 1785, Virginia; Death: 1845, USA Marriage: About 1808, USA Spouse: Amy JAMISON Birth: 31 Oct 1790, Madison, Kentucky Death: 11 Nov 1865, Greene, Illinois Source: patron submission

3.  1800 Census Index/Images (online at Ancestry.com):  can't find.

4.  1810 Census Index/Images (online at Ancestry.com, Image #30 of 53 — a rebound county; extracted by Diana Gale Matthiesen):¤•

1810

KY

Mason Co.

Mason

Roll 7

p. 27/280

Ln. 1

Carrico Dennis

11010-30100-01

8

Wheelwright

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	9 or under	1800-1810	= Nathaniel (b. 1805)
1 male	10-15	1794-1800	= Son A
1 male	26-44	1765-1784	= Dennis (b. 1774)
3 females	9 or under	1800-1810	= Tabitha (b. 1810) = Elizabeth (b. 1808) = Daughter A (b. ca. 1804)
1 female	16-25	1784-1794	= Jane (b. ca. 1784)
1 slave	all ages	by 1810	= ?

5.  1820 Census Index/Images (online at Ancestry.com):  not found, which jibes with them being in Missouri because Missouri Territory didn't become a state until 1821, and there was no territorial census in Missouri in 1820.

6.  1830 Census Index/Images (online at Ancestry.com, Image #78-79 of 95; extracted by Diana Gale Matthiesen):¤•

1830

IL

Greene Co.

Roll 24

p. 42

Ln. 3

Dennis Carico

112 000 010 - 010 200 100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1825-1830	= Thomas (b. 1825)
1 male	5-9	1820-1825	= Dennis (b. 1821)
2 males	10-14	1815-1820	= John (b. 1819) = James (b. 1816/7)
1 male	50-59	1770-1780	= Dennis (b. 1774)
1 female	5-9	1820-1825	= Susannah (b. 1822)
2 females	15-19	1810-1815	= Daughter C = Daughter B
1 female	40-49	1780-1790	= Jane (b. ca. 1784)

7.  1840 Census Index/Images (online at Ancestry.com, Image #1-2 of 8; extracted by Diana Gale Matthiesen):¤•

1840

IL

Greene Co.

Roll 60

pp. 87B-88A

Ln. 28

Dennis Carrico

011 000 001 - 000 100 010

0200000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	5-9	1830-1835	= grandchild?
1 male	10-14	1825-1830	= Thomas (b. 1825)
1 male	60-69	1770-1780	= Dennis (b. 1774)
1 female	15-19	1820-1825	= Susannah (b. 1822)
1 female	50-59	1780-1790	= Jane (b. ca. 1784)
2	persons employed in agriculture

8.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #9 of 23):  South of Macoupin Creek, Greene Co., IL, Roll M432_108, p. 111A, 55/55, enumerated 31 Oct 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):¤•

Dennis Carrico	72	M		Farmer	1700	Maryland
Amy       "	58	F				Ky

9.  1860 Census Every-Name-Index/Images (online at Ancestry.com):  can't find Amy, and I really searched.

10.  Clement L. Clapp, compiler.  1879.  History of Greene County, Illinois: Its Past and Present.  Donnelley, Gassette, & Loyd, Chicago (excerpts online at the Morgan Area Genealogy site):

p. 729-30

CARRICO, JOHN O... was the eighth of a family of fourteen children, and was born in St. Louis Co., Missouri, February 28, 1819. His father, Dennis Carrico, was a native of Frederick County, Maryland.  At an early age he became apprenticed to the trade of a wheelwright, and subsequently became a skillful journeyman workman; attaining his majority, he set out for Pennsylvania, where he worked as a journeyman, and here formed the acquaintance of and married Miss Jane Clark, in 1813 ; in order to better his condition in life, he determined to adopt the West as his future home, and accordingly made his way to Kentucky, where he engaged in his occupation as wheelwright.  It was during the year 1813, that he became a resident of St. Louis Co., Mo., at a period of time, when the entire commerce of the city of St. Louis scarcely footed up to the insignificant sum of $100,000.  Hearing many glowing accounts of the fertility of Illinois, thither he directed his footsteps, and landed in that portion of Southern Illinois, then known as Greene County, since set apart and forming a portion of Jersey County; he necessarily lived a life of frugality for many a year, until such time as emigration flowed rapidly westward, although in after years he became moderately successful as an agriculturist, and became extensively known as a surveyor; his long and useful life ended in 1850 and his ashes repose in the Thompson cemetery, in Greene County.  Mrs. Carrico passed to that world of spirits to which we are all traveling, in 1834, and the survivors of the family, few in number, now reside in different parts of the Union...

This bio may have been OCR'd because it has four glaring errors (when compared with other sources):  John's middle initial, Dennis's marriage year to Jane CLARK, Dennis's death year, and Jane's death year.  The initial 1813 date has to be wrong (it was probably 1803), if for no other reason than that it's internally inconsistent with the narative.  I can come up with a list of fourteen children, based on the censuses, but John comes out the 11th, not the 8th, unless he was not born in 1819.

11.  Messages posted to the Carrico Family Genealogy Forum (online at GenForum.com).

12.  Messages posted to the Veasey Family Genealogy Forum (online at GenForum.com).

13.  Archive of the CARRICO Mailing List (online at RootsWeb.com/Ancestry.com).