The highest % a Republican has gotten in Dubuque County since was Dubya's 43% in 2004 when he carried the state. Willard did get 42%.
Oddly, Dubuque has voted GOP for Governor and Senator (in 1994 it went with Branstad where he got 53%, though in 2010 it went with incumbent Gov. Culver, 50-48%). In 2010, Sen. Grassley carried the county 59-39%.
Here's the 2012 Pres. results with the proper Red/Dem, Blue/GOP colors. Curiously, that one "Red" Dem county in the western part of the state, Woodbury (which contains the Omaha suburb of Council Bluffs) was the only county that swung the opposite way to the rest of the state, voting for McCain in 2008 (49.6-49%) but for Zero in 2012 (49.5-48.5%). Odd, if only because Omaha's Douglas County, NE across the river went for Zero in 2008 but swung back to Willard in 2012.
Oops, I made a big goof in my post #15. Woodbury County, the lone western county in IA that went from McCain to Zero, is of course Sioux City. Council Bluffs is Pottawattamie County and it went 52-46% for Willard (and 50-48% for McCain).