if you have a blog in blogger then go to its c panel..where you will see a "publishing" button. by clicking on this button there is option that you can use your google custom domain in your blog. the domain provided by the google is known as custom domain and you don't need any hosting space to host it...
By being on blogger, arent you already on a "custom domain" ? Google is not giving custom domains for free, and Google is not a domain registrar, but you can set up your web host to forward your domain to your blogger blog.
ready your credit card and visit blogger ,com.type some articles and if you dont have time for it fine,just go to menu ,setting domain there you will find menu in which google can help you to earaed the "blogspot.com" with the sort one,the one that represent your style."yourowndomain.com"
You can do one thing... as u said u have a domain and u want your blog to set up with it.. you can do it with wordpress and then import current blog on wordpress (with your domain name)... it is easy to transfer the blog from Blogger to Wordpress... If more details are required then please lemme know...
Really sorry for replying so late... Its is very easy to import your blogger account to wordpress... as u have got wordpress account and after login to it... go to dashboard.. and then you may find an option "TOOL" in the Menu Bar just above SETTINGS and below USERS click on it and you will find two other options import and export. Click on import to get your blogger account on wordpress. Here is will give u names of blogging service providers... select the blogger option... Here it is where you want to be... Go through authorization process and you are done..