Depends what you mean by "login". Is it filling in a form and POSTing it? HTTP Basic Auth? Javascript magic? Something else?
If it's filling in a form, then you should be able to provide the form content using "method: POST" and "body:" attributes of the
http_probe. You can check that you get a redirect status (e.g. 302) using "valid_status_codes", and it will measure the response time.
You'll have to ensure the body is correctly formatted/encoded, and will probably have to set headers like "Content-Type: application/x-www-form-urlencoded". You can probably capture what you need by logging in while your browser's developer console is open.