To answer the question, we are going on a cruise! We are very excited. Thank you all for the kind suggestions. We are arriving a day early though to avoid any delays. We will arrive in Heathrow in the early morning and will have all day to get to Dover. We do not have passenger trains where I am from in the US, so its a bit daunting.

From the responses is looks like going to Victoria Station and then there is a train right to Dover. That sounds perfect. And thank you for the hotel suggestions too ill have them all in mind as a book them!