I can find no such place as Domgaard (or Domgård), at least not officially and not in any of the major online gazetteers.  It may be a very local name or a farm name.

There are six Albæk's in Hjørring Amt, each in a different parish (sogn); I don't know which this one is.

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

2.  Edmund West, comp. 2000.  Family Data Collection.  MyFamily.com, Inc., Provo, UT (online at Ancestry.com; n.b., West is an undocumented secondary source, so caveat emptor):

Name:	Lars Domgaard	Niels Peter Domgaard
Date of Birth:	19 Sep 1802	27 Jan 1813
Place of Birth:	Hals, Aalborg, Denmark	Hals, Aalborg, Denmark
Name of Father:	Lars C Larsen	Lars Christensen Domgaard
Name of Mother:	Elizabeth	Elizabeth Larsen

3.  Family Tree (online at Phil Lott's web site), specifically, the page for Niels Peter DOMGAARD [link died]. 

4.  The pages excerpted below were formerly online at http://www.ldsep.org, but they're now available only because they're cached at Google.com.  A check at the ldsep.org domain shows the material from that site is to be moved to http://www.mormonhistory.org, but a search there gets no hits for DOMGAARD.  Anyone interested in these families would be well adised to copy these pages to their hard drive for safekeeping until they reappear online.  I cannot post them in their entirety here out of copyright concerns.  The following quoted excerpts are allowable under the concept of "fair use" for academic purposes, and are the only sections containing our subjects:

Ålborg Branch, 1850-Present. On 1 Jan 1851 Lars Chr. Larsen Domgaard and Niels Peter Larsen Domgaard of Hals were baptized in Ålborg by Hans Peter Jensen.  On 20 Jan 1851 several of the new converts were called on local missions to different directions away from Ålborg, among them Hals and Kjeldgårdene... On 11 May 1851 a branch was organized in Hals with Niels Peter Larsen Domgaard as president.  Members of the church in Kjeldgaard, Hasseris, Klarup,and other places in that area became part of the Hals Branch for a short time... Branch Presidents After 1870 almost all of the branch presidents were missionaries from the United States who were serving missions here.  In some instances the branch president also presided over the conference The following were Branch Presidents in Ålborg Branch: Branch President Date Appointed ...   Niels Peter Domgaard 6 Sep 1852 ...

Kjeldgaard Branch, 1851-1867 Kjeldgaard or Kjeldgaardene, also called Kildegaard or Kildegaardene, consists of three small farms situated north of the Guddumlund factory in Guddum Parish, two miles north of the estate known as Guddumlund, three miles south of Storevorde, and about ten miles southeast of Aalborg. As soon as the missionaries were able to establish themselves in Aalborg, they began spreading out to the surrounding rural communities... Christian J. Larsen from Aalborg visited the members in Kjeldgard and held a fast and prayer meeting in the home of Jens Mikkelsen there on 23 Nov 1851. At that time the branch had not been well organized and the members still had to go to Aalborg for meetings.  On 4 Jan 1852 the Kjeldgaard and Hals Branches combined and began having separate meetings in Kjeldgaard.  Lars Peter Larsen Domgaard of Hals assisted in that area...

Is this Lars Christensen or Niels Peter?  Or was there a Lars Peter?

4.  Kathryn Daynes.  Polygamy.  (online at the "FAIR: Defending Mormonism" web site, www.fairlds.org).  Excerpt:

...Or people like Mette Christiansen who came by herself, in her forties, alone and suffered from congestive heart failure.  She became the wife of Niels Domgaard and five months later she died.  His first wife was a nurse and he could see what was happening, they took her in and nursed her in the last few months of her life...

It seems to me a non-sequitor that Mette had to marry Niels to be cared for.  Why couldn't they have just taken her in out of Christian charity?  I don't see this example as supporting the argument for polygamy.

5.  1845 Census of Denmark (online at Dansk Demografisk Database):  Niels Peter Domgaard (æ 33) is unmarried and living alone in "aalbork, Kær, Hals by."