Hi Amy, Sorry that I took so long to reply. I'm afraid that I don't have any more detail about this mysterious daughter other. I have her birth date even more obscure than you: between 1816 and 1820.
However, Elizabeth and the two Campbell children are listed in the 1850 Logan County Census in Washington Township living with Benjamin J. Funny thing is that it shows William's birthplace as Ohio, but Nancy's as Pennsylvania...
Right next to Benjamin's household is his son Solomon's household, so it's pretty certain that it's the right family.
Hope this helps a bit. I know that it helped me: I wasn't sure if the Campbell children were Elizabeth's or not, so I'll look for a Nichols Campbell marriage to see if anything comes up.