I did this exact trip last year around the exact same time.

As long as it is after Diwali and there is no festival etc it is very much doable.

Couple of things you want to do

1) Instead of taking a bus try to take a taxi from Jammu to Katra (should be not more than a few hundred rupees).

2) Get the slip to cross as soon as you get to Katra .... you want to start your climb latest by 3 PM .... it will take you around 5 hours to get to the top. You can rest when you get to the top.

3) Best time to go for the darshan (incase there is a crowd) is late at night .... give yourself a few hours in the line .

4) Start your descent no later than 3 AM .... will still take you 5 hours to come down. Then give yourself a couple of hours to get to Jammu from Katra ... again take a cab (you can get a round trip cab from the Jammu airport itself)