There's a possibility that Elizabeth named her daughter after her sister-in-law, Virginia (GREEN) ROSE.

1.  Robertson County Tennessee, Marriage Index 1839-1880 (online at the Robertson County TNGenWeb site):

MIMMS	Drury	ROSE	Elizabeth	1853
POPE	John	MIMMS	E.	1863

2.  Census Index:  U.S. Selected Counties, 1830 (Broderbund CD-315):  not found, which probably means he's unmarried and living in someone else's household.

3.  Census Index:  U.S. Selected Counties, 1840 (Broderbund CD-316):  not found, which probably means he's unmarried and living in someone else's household.

4a.  1850 Census Index/Images (online at Ancestry.com; Image #40 of 128):  District No. 2, Logan Co., KY, p. 91B, 284/284, enumerated 31 Aug 1850 (extracted by Diana Gale Matthiesen):

Drewry S. Mims

47

M

Miller

2400

Virginia

4b.  1850 Slave Schedule Images (online at Ancestry.com; Image #44 of 66; missing columns contained no data):  District No. 2, Logan Co., KY, p. 395B, enumerated 30 Aug 1850 (extracted by Diana Gale Matthiesen):

Names of Slave Owners	Number of Slaves	Description
		Age	Sex	Colour
Drewry Mimms	1	52	F	B
	1	17	M	B

5a.  1860 Census Images (online at Ancestry.com; Image #59 of 120):  Red River P.O., Western Division, Robertson Co., TN, p. 466A, PN 59, 421/421, enumerated 25 Jun 1860 (extracted by Diana Gale Matthiesen):

E R Rose Extr for R Rose					20,000	40,000
E M Mimms	32	F		farmer		10,000	Tennessee
T Rose	12	M					"
G Mims	6	M					Ky
V R Mims	4	F					Tennessee

E.R. ROSE is Elias R. ROSE, Elizabeth's brother.  Elizabeth's father, Reuben ROSE died just two months earlier, and it appears Elizabeth has come into a sizeable estate.  The fact that Elizabeth has no child younger than four years suggests that her husband died closer to 1856 than 1860.  T. ROSE is Taylor ROSE, who was living with Elizabeth's parents in the 1850 census.  Taylor is too young to be Elizabeth's sibling, but could be her nephew — or illegitimate child.  And a pox on all enumerators who were too <bleep> lazy to take down full names!!

5b.  1860 Slave Schedule Images (online at Ancestry.com; Image #40 of 62; missing columns contained no data):  Western Division, Robertson Co., TN, p. 36B, PN 12, enumerated 20 Jun 1860 (extracted by Diana Gale Matthiesen):

Names of Slave Owners	Number of Slaves	Description
		Age	Sex	Colour
E.M. Mimms	1	13	F	B
	1	5	M	B
	1	55	F	B
	1	25	M	B

"E.M." is the only MIMS/MIMMS slaveholder in the county.

6a.  Census Index:  U.S. Selected Counties, 1870 (Broderbund CD-319):  no Robertson Co., TN, records on CD.

6b.  AIS (Accelerated Index System) Census Index (online at Ancestry.com):  no Robertson Co., TN, records indexed in this database.

7.  Willard Rouse Jillson.  1925.  The Kentucky Land Grants. Filson Club Publ., Louisville, KY (online at Ancestry.com; Broderbund CD-650).  On p. 848:

Part 1, Chapter VII, Grants West of Tennessee River, 1822-1858
Grantee	Acres	Book	Pg	Township [Aliquot, Section]	Range [Twp., Range]
Mimms, D S W	160	3	67	N W Qr Sec  5	T-1 R-6 E
Mimms, Drury S W	160	6	230	S E Qr Sec 22	T-1 R-6 W
Mimms, Drury S W	160	6	230	N E Qr Sec 22	T-1 R-6 W
Mimms, Drury S W	160	6	231	N E Qr Sec  3	T-1 R-5 E
Mimms, Drury S W	160	6	231	N E Qr Sec  3	T-1 R-5 E

It's too bad, for us, that no county or specific dates are given.  Drury is the only MIMS/MIMMS listed in this Chapter of Jillson.
It's amazing, considering how much work Jillson did with land records, that he was apparently clueless as to how land designations worked:  under "Township," he gives the Aliquot and Section; under "Range," he gives the township and range, but leaves out the direction (N or S) of the township from baseline — though it is presumably "N," it still should be designated.  For example, the location of Drury's first land grant should read NW ¼ S5.T1N.R6E and should be read outloud as, "north-west quarter of section five in township one north, range six east."