To indexing the website in google is depend on the how much authority your site has with google,
you can also submit your link in G+,twitter and facebook to crawl fast
otherwise you can ping it with lot of online tools are available.
i don't think redesign will help to your website, just create the user friendly,attractive and creative website
f which you want to shown to the critic.
but steel you have create the new website then use the latest technology(Bootstrap or Responsive)