I know you just want your Dr to prescribe you something, but sadly, that's almost never the answer. And I'm speaking as someone for whom medication has been very important... But I have a psychotic illness. And even with a severe psychotic illness, crucially important was psychological support... In my case my dr spending the time talking to me, listening to me, supporting me... For years on end.
What your dr (GP) can do is write a psychology referral under Better Access so that you can get subsidised appointments with a psychologist. You'll need to book a long appointment, a double appointment, and ask for a Mental Health Treatment Plan and psychology referral. In the process you can talk about medication and whether it has a role in your care. Medication has a lot of downsides, and talking therapy is usually just as effective as medication. Your dr will let you know if there's something particular about your circumstances that means medication might be helpful. Speaking as someone who responds well to psych meds, I'm also aware that there are people who have difficulties with side effects, and it usually doesn't help people... At best, antidepressants have an effect in 1 out of 5 people who take them for depression.
You mentioned not having a car... If you've seen a GP at the practice within the past year, you can have a 15 minute telehealth appointment on Medicare. And if you register for MyMedicare with that practice, you can have long telehealth appointments. MyMedicare is a new government program that I personally don't like, but part of it is that if you register with a practice, and you can only register with one practice, then you can have long telehealth appointments on Medicare. So if you wanted to do the whole Mental Health Treatment Plan appointment by telehealth, it would be worth ringing the practice and working out how you register so that you're eligible for the full rebate.
I'm not sure where you are, sometimes it can be hard to find a psychologist who is taking on new clients. You could ask your GP if they can help you find a psychologist, if you're not sure how to go about it. There may be other resources in your community your GP can tell you about, depending on your particular situation.
Recovery is a long road, but most people get there. I've been in very dark places, homeless, but I now have good stable mental health, a Master's degree, and nobody would guess where I've come from. You will get there, but it takes time, and sometimes you just need to hang in there. Take care.