What do I need to have in case our midwife doesn't show up in time?
Just in Case?
Your birth kit for the chux pads, etc. Maybe a brief conversation with your midwife now as to what your partner can do to assist you and under what circumstances you'll want to call 911. I know several people this has happened to (and to be fair I know a LOT of home birthers so I'm not implying it's common or anything) and really when the baby comes that fast there is rarely any sort of problem. Just keep mom and baby warm (throw a receiving blanket over baby and keep baby on mom's chest). Don't cut the cord. As long as baby is breathing okay, there's not excessive bleeding and everyone stays warm you can generally sit tight until the MW gets there.
At the home visit our midwives give us a sheet called "What to do if baby arrives before the midwives". I haven't gotten mine for this birth yet but from last time what I remember is 1) If baby is coming that fast it *usually* means there are no complications 2) Don't worry about cutting the cord and 3) The most important thing you can do is keep the baby warm.
I have an "instant labor" box in addition to my other birth kit box - and directions from the MW posted in a prominent place. Basically we were told to put down a shower curtain, flat sheet and chux pads - get on hands and knees - when I feel like pushing lift up one knee to get in a semi squat and catch my baby - sit down (don't lay down) and place baby on stomach, rubbing her back, then baby to the breast. This of course with the assumption that midwife is on the way. She specifically said not to call 911, get on the toilet or get in the tub/shower during labor.