While posts in Tumblr can certainly be queued, I still want to discuss this a bit more as the frequency between posts are quite strange. If you look at her posting frequency, it seems that up until last week the posts were queued to post basically daily. I'm attaching screenshots of how the Tumblr queue works. Basically you can pick the number of posts you want to queue up each day. It appears that she didn't use the queue system here for this latest post because several days have gone by before the previous posts, whereas for those actually in the queue at least 1 post would queue up each day. It looks like if she did post this herself before she died, it would have to be via an exact schedule, which I also show a screenshot of how scheduling in Tumblr works. You can schedule at an exact day and time. But it seems like strange behavior that she would be basically queueing up posts at least once a day up until 1 week ago, and suddenly a week later a new post pops up. It's definitely possible that she manually scheduled this one but there must still be something about this post that makes her schedule it almost a month later and that itself is very interesting.
I think it might be worthwhile to check with someone that works in Tumblr on when exactly her last login/request was to the Tumblr server, and check the IP address of that last login/request since this could potentially be very important evidence.