Either John's birthyear is in error or the census-enumerator made an error because a son under age 10 does not occur in his parents' household in the 1800 census. 

1.  Census Index:  Colonial America, 1607-1789 (Broderbund CD-310):  Godfrey not found.

2a.  Census Index:  U.S. Selected Counties, 1790 (Broderbund CD-311):  Godfrey not found.

2b.  1790 Census Index/Images (online at Ancestry.com):  no WOMER/WOMMER/WOOMER found, at all.

3a.  Census Index:  U.S. Selected Counties, 1800 (Broderbund CD-312).  Please see my WARNING regarding use of this database (the numerical data have the genders switched).  Yes, in both of these cases, the switch makes no difference, but I like to point out the problem at every opportunity. 

1800

Wommer, Godfrey

PA

Northumberland Co.

p. 845

01001-0100100

3b.  1800 Census Index and Digital Images (online at Ancestry.com; Image #5 of 6; extracted by Diana Gale Matthiesen):

1800

Wommer Godfrey

Northumberland Co.

Beaver Twp.

p. 845/190

01001-01001-00

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	10-15	1784-1790	= John (b. 1793?)
1 male	45 or over	in or bef. 1755	= Godfrey (b. 1746)
1 female	10-15	1784-1790	= Daughter A
1 female	45 or over	in or bef. 1755	= Wife

Has the enumerator placed John in the wrong age category?  Or is John's supposed birthyear incorrect?  The only other WOMER/WOMMER/WOOMERs found were Godfrey's sons:  Jacob WOMMER, who was also in Beaver Twp., and Daniel WOOMER, who was also in Northumberland Co. (in Mohantango Twp.).

4.  1810 Census Index and Digital Images (online at Ancestry.com; Image #4 of 5; extracted by Diana Gale Matthiesen):

1810

PA

Mifflin Co.

Derry Twp.

p. 1030

Godfrey Woomer

20101-00101-00

30 20 0 0 2 4 2 6 0 0 0

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	9 or under	1800-1810	= grandsons
1 male	16-25	1784-1794	=  John (b. 1793)
1 male	45 or over	in or bef. 1765	= Godfrey (b. 1746)
1 female	16-25	1784-1794	= Daughter A?
1 female	45 or over	in or bef. 1765	= Wife (b. 1745-55)
30	Woollen Cloth
20	Flaxen Cloth
0	Cotton Cloth
0	Hempen Cloth
2	Spinning Wheels
4	Common Sheep
2	Horses
6	Cattle
0	Looms
0	Hand Cards
0	Sugar

Young children in the home of an older couple are usually grandchildren.  Also in Derry Township:  Anthony WOMMER.

5.  Census Index:  U.S. Selected Counties, 1820 (Broderbund CD-314):

1820	Womer, Godfrey	PA	Berks Co.	Lower Bern Twp.	p. 38
1820	Woomer, Henry	PA	Mifflin Co.	Wayne Twp.	p. 182

Is this really our subject?  This isn't where he's supposed to be.  Or is he living with his son, Henry?

6.  WorldConnect (online at RootsWeb.com).

7.  Raymond Martin Bell & James Allen Woomer.  1980. The Wommers of Saarland and Pennsylvania:  also Spelled Woomer, Womer, Wummer, Wumer.  Self-published, Washington, PA.  Not seen (as cited by J.T. Womer in his file online at WorldConnect).