Your question is not as specific to biology as you may think. The hawk-dove game is a type of game in game theory, a field of mathematics. Game theory is used in biology, in economics, in psychology and many other disciplines.
The hawk-dove game is often called the chicken game. If a game is defined as a chicken game, then it has an equilibrium different from 0 or 1. Otherwise, it may not.
You need to fully specify the scenario of interest to figure our what type of game we're dealing with to know what type of game we're dealing with and what are the possible equilibriums.
For more information, have a look at the mathematical field of game theory.
You specific scenario
The scenario as written in your post is not fully discribed. In your question, you define the doves such as they have a fitness (or a payoff in game theory terms) of 0, whatever is the state of the population. For such case, of course, a frequency of doves of 1 cannot be an ESS. However, under such case, you are not dealing with a hawk-dove game. I suspect you misunderstood the game as defined by Dawkins (it is also possible that Dawkins did not fully define the game he's talking about).
In short, I can't say much else than just "read more about game theory". However, you might want to cite exactly Dawkins so that we can understand exactly how he describes the specific game at play and comment on the expected outcome.