Hi Serb!
I have used the extended family exemption (
here) to travel to Canada to see my boyfriend, who's a Canadian citizen, from the UK. I visited December 2020 to March 2021.
There is a form you need to complete (
here), which you and your girlfriend will sign a declaration.
This will also need to be notarised - we used a lawyer for this, you'll just need to have a meeting with them to verify your relationship. Examples of evidence are: chat logs, flights/reservations to see each other in your relationship, photos. Flight/accommodation reservations are an easy way to prove you have physically been in each others' presence.
I am going through the process again now as the exemption only lasts for 6 months. The exemption itself doesn't permit you to travel - you also need a valid visitor visa and a quarantine plan to be allowed to fly.
Good Luck!