You would be better off using curl or wget to simulate a login and capturing the response time of that.
+1 to handat. WLST would be completely the wrong tool for this. Use curl, or a simple python program using the requests library. Here's a sample that uses the requests library - it's commented so you can see which bits you'd need to include just to test login time.
Can you please provide a sample code so that it would be helpful for me to try understanding what curl is.
curl is a command line tool that can perform http requests.
Here's an example syntax to connect to a site with username/password:
curl -c cookie.txt -d "LoginName=someuser" -d "password=somepass" https://somesite.com:9704/analytics
And here's a site with more samples and tutorial: http://www.yilmazhuseyin.com/blog/dev/curl-tutorial-examples-usage/