The 28th of this month?
Get a train from Dover Priory (the closest station to the port) and go to St Pancras International. There are numerous trains with either no change or one change. You can see the schedule and pricing here:
http://www.nationalrail.co.uk
At St. Pancras, I would just grab the tube (Piccadilly Line) direct to Heathrow. Make sure you get on a train going to Heathrow 2,3 and 5.
The whole trip will take about two hours and thirty minutes.
However.....the 28th is a Sunday and there could be disruptions on the line. If that's the case there is a bus service from Dover to Heathrow with a change in London. This will take longer.
http://www.nationalexpress.com
There's a coach that leaves Dover at 7:15am and will get you to Heathrow just after noon. Later coaches arrive too late.
I would try to train first.
Have you also considered a private transfer.....ship to terminal?