I thought about a similar thing. I think students doing that would tend to have to repeat coursework at the new school, so you'd most likely loose a year or so. You can try to do it, but it may also make sense to get a PhD from Purdue and then try to get a Post-Doc at a more reputable school?
What I've described was once my backup plan, but now it's sort of what I've settled on doing. It'd be worth asking Purdue students to see if they do well in the Post-Doc search, because if they do, then this route would have you spending 5 years in a phd program at 20k/yr, and then 1 year in a post doc at 60+k/yr, as opposed to 6 years in a phd at 20k/yr and then still maybe having to do a post-doc before getting an asst. prof. position.
Sorry, I wish I could comment more on this topic more specifically, but I hope this helps marginally.