It's easily do-able in that the time you have. As another respondent has said, it's best to get a taxi firm to meet you as otherwise you have the taxis from the rank which are terribly expensive. Get the taxi firm to meet you inside the airport, with a nameboard. It will cost about £5 more but it's easier. Going into the castle grounds might be an option but it's unlikely you would be able to get into the state rooms or to see the dolls house because the queues are horrendous. There's a nice walk along the river and also there are boat trips which take about an hour and are nice to do - you get great views of the castle from the river. Eton is pleasant, but personally I wouldn't bother. I would stick with a quick walk around the castle, down to the river, along the river and lunch on the terrace at Browns - weather permitting.