We can definitely use your existing logo, brochure and other material for your website development. In fact, this is a good idea.
The reason this is a good idea is that you have already put time, effort and money into those materials. Those materials have likely already become part of your brand and your message. Using them in your website makes sense because it will be a cohesive message between printed materials and your website.
No matter how your customers find you it is important that they see the same branding.