Redirecting to another page
Well, for starters, your redirect will never work if you pass in both $key and $page, as you're asking for the following:

1. is not isset($page)
2. is not empty($page)


Which means that the redirect will happen only when $page is NOT set and NOT empty. Because empty() calls isset() internally, you should only need this:

if(!empty($page))


Additionally, you're not managing your buffers. Ideally, you should use the ob_ functions as well as headers_sent() to check if headers have already been sent. If you don't manage your buffer, you're very likely to hit the infamous "Cannot modify header information - headers already sent" error. This post goes into further detail on how to fix that error, especially using the ob_ functions. 

Aside from all that, your construct is doing nothing. If your Redirect class only has the to() method, perhaps you're better off making it a standalone function, or adding additional functionality.