My (23M) girlfriend (22F) needs space while dealing with a family crisis. How can I proceed?

My girlfriend and I have been in a relationship for a little under one and a half years. She has struggled with depression and severe anxiety for most of her life and has been taking an SSRI for around six months. She also has a tendency to isolate herself when she’s not doing well.
When we first got together, her depression and anxiety were significant, but she improved immensely throughout our relationship. Things between us were good and her mental health was under control. We were making plans together, spending time together normally, and I had no reason to think that our relationship was in danger.
A couple of months ago, her family found out that her grandmother has cancer. This was obviously difficult for her, and she had been struggling emotionally since then, but our relationship was still okay despite everything. We continued being together and making plans.
The situation changed last Wednesday. Her grandmother’s condition suddenly got much worse and she is now bedridden for most of the time. My girlfriend has effectively become her primary caregiver because the rest of her family isn’t available to help much.
That was the point where things between us changed. Less than a 24 hours before this, we were making plans for the weekend and things felt normal between us. Then, after her grandmother’s condition deteriorated, my girlfriend was clearly very stunned by this and not ok.
Yesterday, she texted me saying that she needs some time and space. She said that she needs to deal with everything on her own right now and doesn’t know if she has the capacity to be in a relationship while all of this is happening.
At the same time, she told me multiple times that she still loves me. She said she wants to get better and eventually be able to get back into our relationship, but that she simply can’t handle the relationship right now on top of everything else.
Our last conversation ended with her telling me that she loves me. We haven’t spoken since.
I don’t know how to proceed. Is my relationship doomed?
For people who have experienced something similar, how did you handle this? How did it go?

Some things that might be worth mentioning:
As previously stated, she always had a tendency to isolate herself when she is not ok, but it never went this far and she always came back from it not long after.
She is and always were a very lonely person. She was always bad interacting with people and we strongly suspect she might be mildly autistic. The closest friend she has lives very far away and replies to her texts twice a month. She doesn’t have any other friends, is currently unemployed and out of college. The only people in this world she is close to are me, her brother and both her grandparents. Her father’s side of the family is not a part of her life, including himself. Despite all of this, before her grandmother got worse, she was stable and had an active life. She had been studying to try and get into college and recently started going to the gym, something she was very excited/invested about and doing consistently.