Hi nj..
I was pretty much on the same path as you are right now... I also got the mini as mentioned earlier and was considering either a front and/or rear rack. I'm not sure if you've come across the threads about them in relation to a Downtube Mini but here are some that I've found. Hope it helps.
This one's about the front rack from Nashbar and some debate about its durability.
http://www.bikeforums.net/showthread.php?t=413439
This one's about the rear rack being installed on a Mini even if it has rear suspension.
http://www.bikeforums.net/showthread.php?t=392503
Sorry, don't have any dogs (hopefully, someday I'll have one) so I have no clue with that one.