Under both the IRC & UPC you may not have a horizontal offset in a vent line until the line reaches an elevation equal to or greater than 6" above the flood level rim of the highest fixture served by that vent.

Normally the lavatory bowl is the highest fixture served by a bathroom vent and generally the flood level rim is even with the top of the counter surface, however if you have a vessel sink the flood level rim would be the top rim of the vessel.

Assuming for the moment that you have a standard lavatory bowl set in the counter top, you could then install a sanitary 1/4bend 6" above the counter top, run the line into the next stud cavity, turn up, then turn back at a convenient point above your cabinet and reconnect to the existing vent however there are a couple other points that must be considered.

Under the IRC if the extended length of the offset extends the total length of the vent over 40' total developed length you would be required to increase the diameter of the entire vent one nominal trade size of pipe, but it is very rare that a vent line will exceed 40'.

Under the UPC if the combined length of the horizontal offset exceeds 3' you would be required to increase the vent one nominal trade size,,,

But not to worry, there is a very easy solution.

Rather than cut the vent above the counter and make a horizontal offset you can cut the line lower, then install an 1/8bend (45deg elbow) and run the offset into the next stud cavity at a 45deg angle. You then install another 1/8bend turning vertical and install another 1/8 bend and run the line back at a 45deg angle above your cabinet.

By running the lines at a 45deg angle they are still classified as vertical lines and you would not have to be concerned about the elevation above the flood level rim or the total length of the vent line.