-BAUGH is an Anglicized spelling of -BACH.  Most Germans in the U.S. with surnames ending -BAUGH, will turn out to have been -BACH in Germany.  Surname DOSBACH does occur in Germany.
John is the English cognate of Johannes, Johann, or Hans; no 18th or 19th Century male in Germany would have been given an English name like "John"; the transformation had to have occurred in the U.S.
They are said to be from Saarland, Germany, but the one primary record I have that shows anything other than, "Germany," is daughter Mary in the 1870 census, which has her born in Baden.

Mary's birthdate cannot be correct if she had a child in 1830, and the censuses also dispute this date (see below).
Mary and Elizabeth are English given names, cognates of German Maria and Elisabetha; no 19th Century female in Germany would have been given English names, the transformation had to have occurred in the U.S.
KAUGHMAN is an Anglicized spelling of KAUFMAN; the KAUGHMAN spelling is very rare in Germany, while the KAUFMAN spelling is common.

— born in Paris Twp., Stark Co., OH:
3.  (Daughter A) DOSBAUGH, b. 1830-35
4.  John DOSBAUGH, b. 10 Jan 1834; d. 27 Mar 1916
5.  Margaret DOSBAUGH, b. 1837/8
6.  Samuel DOSBAUGH, b. 1839/40
7.  Sarah "Sallie" DOSBAUGH, b. 12 Feb 1843

1.  Marriage Record:

2.  1830 U.S. Census Index/Images (online at Ancestry.com):  not found.

3.  1840 U.S. Census Index/Images (online at Ancestry.com, Image #7-8 of 28; official enumeration began 1 Jun 1840; mis-indexed "Darbaugh"; extracted by Diana Gale Matthiesen):-

1840

OH

Stark Co.

Paris Twp.

pp. 21B-22A

Ln. 15

John Dasbaugh

111 000 010 - 111 000 100

0001000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	= Samuel (b. 1839/40)
1 male	5-9	1830-1835	= John (b. 1834)
1 male	10-14	1825-1830	= Son A?
1 male	50-59	1780-1790	= John
1 female	4 or under	1835-1840	= Margaret (b. 1837/8)
1 female	5-9	1830-1835	= Daughter A
1 female	10-14	1825-1830	= Mary (b. 1830)
1 female	40-49	1790-1800	= Mary
1	person employed in manufactures and trades

4.  1850 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #3 of 16):  Johnston Pct., Dist. No. 48, Clark Co., IL, Roll M432_100, p. 272A, 1538/1538, enumerated 17 Oct 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):-

John Dashbaugh	65	M		Farmer	800	Germany
Mary      "	45	F				"
Mary      "	19	F				"
John      "	16	M		Farmer		Ohio
Margaret  "	12	F				"
Samuel    "	10	M				"
Sarah     "	8	F				"

5.  1860 U.S. Census Every-Name-Index/Images (online at Ancestry.com, Image #19 of 22):  Casey P.O., Johnson Twp., Clark Co., IL, Roll M653_162, PN 143, 490/1, enumerated 22 Jun 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):-

William D Crouch	60	M		Farmer			Maryland
Mary        "	30	F					Germany
Sylvester   "	18	M		Laborer			Illinois
Mary Doshbaugh	57	F					Germany	insane
Jimmy Deford	60	M					Maryland

At the time, "insane" was a blanket term that included old age dementia, alcoholism, retardation, etc., anything that made someone mentally abnormal. 

6.  1870 U.S. Census Every-Name-Index/Images (online at Ancestry.com):  can't find.

7.  Find-a-Grave: Entries (online at findagrave.com):

Name	John Dosbaugh	Mary Dossbaugh
Birth	unknown	unknown
Death	4 Aug 1854	8 Dec 1873
Burial	Mount Cemetery Johnson Twp., Clark Co., IL	Salem Cemetery Bluff Creek, Johnson Co., IN
Inscription	JOHN DOSBAUGH DIED AUG. 4, 1854 AGED 69 YR 6 MO
Spouse		John Dossbaugh
Memorial #	52853827	52216922

John and Mary were not linked, so I submitted the links (5 Dec 2018).  Mary's daughter, Sarah (DOSBAUGH) SURFACE, was living in Johnson Co., IN, from 1863 onwards.  Is this how Mary came to be buried there, rather than in Clark Co., IL?

8.  Public Member Trees (online at Ancestry.com):  The file that shows our subjects as born in the Saarland gives no documentation for that location.