FCC Part 15 Class B Declaration of Conformity (DoC)
It depends on what it is, look at what your device is in the table:




  Verification
  
  Verification is the easiest and quickest authorization route.
  Verification just involves you sending your product and any required
  auxiliary equipment and cables to a test lab. The lab spends
  approximately 1-2 days measuring the radiated and conducted (if
  required) emissions coming from your product. If all is well, they
  generate a test report and send it to you. That’s all there is to it.
  You’re now at liberty to label, market and sell your product.
  
  Of the 1000 or so FCC test labs around the world, you can select any
  of them to do this job. From the FCC’s perspective, there are “2.948
  listed” test labs and “accredited and FCC recognized” test labs. The
  difference is that trusted independent 3rd party companies are used to
  inspect accredited labs to verify a certain level of competence and
  that procedures are implemented and being followed properly. For
  non-accredited, registered test labs, no such 3rd party inspection
  take place. Approximately 2/3 of FCC test labs around the world are
  not accredited.
  
  Declaration of Conformity (DoC)
  
  Not to be confused with the Declaration of Conformity for Europe,
  which is completely non-related, the DoC method for the FCC covers
  certain types of electronic equipment.
  
  If your device is in a category that allows the DoC authorization
  route, the key here is that you need to select an FCC accredited test
  lab. Test labs that are only ‘2.948 listed’ with the FCC and are not
  accredited, are not allowed to test devices using the declaration of
  conformity authorization route.
  
  Before these new rules, “Listed” (or non-accredited) test labs could
  get around this requirement by instead undertaking ‘certification’
  testing on your device. But that option will no longer be available to
  you or to the test lab when the rules come into full effect. So,
  products subject to the ‘DoC’ authorization route will only be able to
  be tested at an accredited lab.
  
  Certification
  
  Certification testing requires an application package of test results
  plus other documentation be sent to a special test lab called a
  Telecommunication Certification Body (TCB). Both accredited and
  non-accredited test labs could previously do the testing for
  certifications. After these rules come into effect, only accredited
  labs will be able to perform the testing. It’s worth noting that TCBs
  can also perform the testing themselves as well as issue the
  certifications.


Source: EMC fastpass




  Are we required to use an accredited lab for the Class B unintentional
  measurements?
  Ultimately, my company's you know what, is on the line as the
  certifying party. So why can't we take the readings, and certify?


If the product being tested only needs verification, then you could test at a lab that has been registered with the FCC. If you need a DOC, then you'll need to go to an accredited lab. 

Of course, you can always test in your lab before you send the product out for testing to make sure the testing goes smoothly and you don't have to do a second round.  


  The only place I read that the Class B DoCs must come from accredited
  labs, are from the websites of accredited labs!


No, the FCC also tells you that you need DOC's from an accredited lab:


  Q:  I don’t have the expertise in house at my organization. Who can
  provide FCC equipment authorization? 
  
  A:  Unless you are fortunate
  enough to have an accredited in-house FCC laboratory in your company,
  the best choice is to involve a third-party FCC lab at the design
  stage and then follow through with testing of your product at the lab.
  
  Q:  Is one lab as good as another?
  A:  There are many EMC labs around the world. In accordance with 47 CFR 
  2.948, the FCC list labs that the FCC has on file for FCC Verification 
  equipment authorization. For any FCC work, your lab should be on this list.
  
  Furthermore, if the device requires Declaration of Conformity
  equipment authorization, the lab must be ISO/IEC 17025 Accredited. An
  accredited lab has been audited by a third party such as the American
  Association for Laboratory Accreditation to the international standard
  for good laboratory practice ISO/IEC 17025.  
  
  The following website: http://www.fcc.gov/oet/ can be used to find an
  FCC lab that is listed under 2.948 or Accredited for FCC work. Search
  under “Test Firms”. Then search by the level of accreditation needed.


Source: FCC FAQ's