Battled the sleet, horizontal hail and winds today for 12 miles with 2 miles at LT effort (5 mins recovery) then 4 x 1 mile at LT effort (4 mins recovery). Paces a bit off - wind and Wednesday running!
There are plans for people already doing the distance, or thereabouts, but you won't find them under beginner plans. They're generally aimed at more experienced runners. For instance, I'm following Greg McMillan's 10k plan for 4-5 runs per week and my longest run in the first week was just over 9 miles.
Are you following a plan at the moment? You could, for example, do the last 6 weeks of the program twice. This would include taper weeks to avoid burnout and you would start building again after 6 weeks. Though if you can knock out 13 miles in 2 hours as a long slow run, you should be able to nail 1:50 in a race.