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Welcome to Sevenoaks - it is a lovely area to be in with children.
I think some of the GPs in Sevenoaks have a strictly defined catchment area - they won't take on new patients from outside it. When I gave mine my new address they checked I was still in their area (just central sevenoaks)otherwise I had the impression I'd have to move GP. I've not heard anything bad about any of them - hope you find one.
There are quite a few good day nurseries - some you seem to have to put the childs name down before birth (Acorns in particular which is popular as it is next to Sevenoaks Primary school) - I can only suggest ringing round them all to find out if they have space. I've heard good things about Teddies and Squiggles in Sevenoaks too and the montessori nurseries.
Re: GP - I'm with Amherst Medical Practice - they have a surgery in Brastead which isn't too far from you. I've been with them all my life and in general are pretty good - if it's an emergency I've never had any problems not getting an appointment the same day.