I can see both sides of the arguement. While it may seem heartless to begin disposing of stuff now, you're the one who has a deadline to deal with when the time does come...not your aunt. But, I can understand her having difficulty dealing with things. Seeing stuff go can feel like letting go of her sister before she passes. But, it's difficult no matter when you do it.
When my mom passed, my dad immediately began getting everything that was hers out of the house. I was the one he charged with the task...even though I wasn't ready to do it. Most of it, I ended up taking home with me to CT until we had time to decide what to do with it. I was angry with him at first, until I realized that the reason he was doing it was that it simply hurt too much to see constant reminders of his loss.
Everyone deals with loss in their own way. None of us has a right to dictate to others how that's done. Had I insisted that my dad keep things (which I knew he'd eventually wish he had), it would have caused him more pain. So, I kept them and waited. When he was ready to see them again, I brought them back. In your case, there's nobody else there in the house to see things. So, it comes down to you.
My advice would be to at least make a mental note of those items that mean something to you on a personal level...things you'll likely want to keep for yourself. Once you've done that, perhaps you can invite your aunt (and any other close relatives) to see if there are any items they'd like to have as a keepsake. It could prove to be healing for all involved. If there are items that are of no use to anyone, I'd go ahead and pitch them now to give yourself a head start. But, again, that's your call.
As you go through things, you can make lists of what you want to do with each item. If you're planning to give things to good will, you might see about whether the specific place you have in mind will pick things up. Since you have no reliable transportation witrhout having to pay for it, this would make things easier for you. Are there items that you could sell? If so, perhaps a weekend tag sale would bring in a few bucks...provided you have the energy to deal with it and there's enough to make it worth the bother. If not, then a curb alert on craigslist when you put them out will clear things away rather quickly. (We did that with items that were left when we were ready to move and it went almost as fast as we could put it out.)
Having so much already on your plate, it may feel like too much to start now. But, it could prove healing for you and allow you to relax a bit more when the time does come. Again, it comes down to what YOU decide.