We already had four male Pokémon professors, from Generation I up to Generation IV, so having a female Pokémon professor again for X and Y is good enough, for a change at least.
And I also agree with the more involvement of the professor in the story of the game or in our journey. Professor Juniper is a good example; she's been involved in the issues of Unova, so the next professor should be the same too, but more.
Research? The new professor would probably research about the genetics of Pokémon, learning more about their genders and chromosomes. I suppose that would explain and answer the past questions regarding the different appearances of Pokémon in terms of gender, or the gender counterparts of Pokémon. Pokémon such as the Nidoran family or Gallade and Gardevoir would possibly be explained by the new professor.