You can use the same custom domain for WordPress blog.
Steps to follow (if you want to go with self hosted WordPress):
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First purchased a hosting for WordPress from any hosting company.
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Install WordPress on temporary URL provided in hosting account.
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Import all the posts and comments from blogger.com blog by using default imported tool present in WordPress dashboard.
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Follow remaining steps mentioned in this article.
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Change the DNS in domain registrar for hosting account.
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Final step, change WordPress URL from temporary to custom domain.
Note: If you want to same design like your blogger blog in WordPress, then you may need to hire some theme developer professional.
Hope above steps helpful to you.