You should be alright. The ship will wait if it is, as I assume, a coach arranged by them. The normal time to reach the docks is one and a half to two hours although this weekend it took me nearly three hours to reach Southampton from Heathrow because of the bank holiday traffic so it will depend on the day as to whether they are pushing it a little. An alternative is to make your own way earlier to the dock and you can do this by scheduled coach which will take a while but is cheap, train which is convoluted from Heathrow or taxi (which should be arranged from the Southampton end) and will cost about £70.
I would stick with the guaranteed way and not worry Neil
If it is a cruise ship organised transfer then the ship will wait. If you arranged it yourself then the onus is on you to get there in time. LHR to Southampton should be 1 1/2 hrs drive on a clear run.
If you look on the Eavesway website, then 13:45 is the normal time of departure from Heathrow for the Cruiselink service. You should have no problem and the ship will wait if late. The coach starts from Victoria coach station at 1p.