Tracking down family clues about Norwegian locations gives the researcher a challenge!
First, your thought that Gulbransen might be a variant of Gudbrandsdalen, would be my first guess as well. Traditional districts like Gudbrandsdal in the Norwegian county of Oppland, were used as an easily recognizable location – similar to saying your American relatives were from the Midwest. That narrows your search somewhat, but you’ve still got a lot of work.
So one normally looks for shortcuts. First figure out when she immigrated. Your Barbro Johnsen Rose (born 1863 & married first to Norman and then to Andrew Rose) appears to have left Norway in 1881 (according to the 1900 US Federal Census).
Next you might check Norway Heritage emigration records ( http://www.norwayheritage.com/ ) to see if you can find her. Name was likely recorded as Johnsdatter rather than Johnsen, which is probably an Anglicized version.
Failing the above, one can fall back on a parish-by-parish search in the parish emigration records for a Babro/Barbara with a father named John who left Norway in 1881. Parish-by-parish through all of Gudbrandsdal is a bit of work.
If that comes up dry, you may need a broader search in Norway. Other possibilities include a farm names, parish names, municipality names, or county names.
Nothing comes close to Gulbranson in parishes names, municipality names, or counties. That leaves farm names.
Rygh’s “Norvegian farm names” (see https://www.dokpro.uio.no/rygh_ng/rygh_form.html ) suggests a possible similar farm name of Gulbrandstuen in Sødorp parish, Nordre Fron municipality, Kristians amt. With further information (birthyear of Barbro, names of other relatives, or year of emigration) I would normally look through the records for Sødorp parish to see if family lived there. That said, this is a bit of a forlorn hope.
Hopefully someone else has a better solution.
Best wishes!