You need to start getting the miles now. I went from having done a century to riding 730 miles in 4 days (unfortunately the goal was 890 in five days). I'd say it was doable, but you need to get training now. You need to build up to a distance of 100km/60 miles soon, and start doing that distance in one ride most weeks, plus other shorter rides. With that base, you can try your first 100mile ride. You'll want to do that distance a few times at least, and one week do a 100 miles 2 days in a row. When you have done that, you'll have a good insight into what you can do.
If you haven't done much long riding, maybe start with 10 miles every second day, then 10 miles every day, then add another 10 mile ride later the same day so you are now doing 20 miles a day.
Find out how the ride will be staged. If the distance between stops will be 40 miles, get to riding that distance non-stop as soon as you can.
You can certainly do that distance on a hybrid, though drop bars are preferred by most long distance cyclists. For the actually ride, you will want a light bike with narrow wheels and lots of choices of hand positions.
You are going to have to push yourself, and spend long hours on the bike. At the end of these rides, dismounting can be a challenge without a baby. I would not put a baby seat on a bike with a cross bar for these sort of rides, because dismounting could be a huge problem. The bike will want to tip over, and you will be trying to lift a tired leg over the cross bar. I'd think there was a huge risk of dropping the bike and baby or kicking the baby in the head - sorry, but you will be tired. I think a trailer would be the best solution, and then you can train on whatever bike you like, and when you uncouple the trailer, you will fly! Also as you will be on the road for hours, your baby/toddler can sleep/wake/look around/amuse himself with colouring books or whatever
http://www.halfords.com/cycling/bik...iler?cm_re=mmcycling-_-accessories-_-trailers
I'd repeat your question in the family forum here, for more expert advice on cycling with kids, eg
https://www.cyclechat.net/threads/kids-trailer-any-recommendations.189785/
Edit: image added curtesy of
@ianrauk