I assumed I did not get the FKT when I did the route since I did not get the CR for the strava segment of the ascent but after further investigation it looks like this time is the Round Trip FKT. There have been faster ascent times than this but they have either been significantly slower on the descent or taken a different, longer way back down, again making the RT time slower.
It would be great to start getting FKT's posted here for this route instead of having to comb through the various segments on Strava. I have been searching the Strava segments along with reading the route description in which Tom Ferrell posts a RT time of 59:4 and I cannot find a faster round trip time than my 58:32 time.
This effort was from the large trail info sign on the east side of the Dog Mountain parking lot to the true summit (past the viewpoint where the majority of people stop) and then back to the sign. My ascent time to the true summit (not the ascent strava segment time) was 38:52.