I'm going to be unpopular and say ... it depends.
We travelled a lot when our kids were in the "under-2" category (though on a number of shorter trips rather than one extended one). Between the two kids, they hit Russia, Indonesia (northern Sulawesi), Morocco, Fiji, Madagascar (north and south), Egypt, Turkey, Jordan, Singapore, Iceland and a bunch of Europe before they (respectively) were 2. Madagascar and Indonesia were definite malaria and health risks when we went - but we went prepared.
There is a pediatric form of Malarone that can be given to kids under 2 to deal with the malaria risk. It tastes nasty (the coating on the tablet dissolves before the kid - or at least mine - manages to swallow it) but if you bury the tablet in a piece of soft candy, it goes down ok. (crushing it in applesauce, which is what the peds will recommend, does NOT work - just results in the kid hating applesauce for at least 6 months!).
You DO need to be very very cautious about dehydration - but some rehydration solution and a cautious approach handle most situations. Remember that germs in moderation are a GOOD thing and will make the kid more reslient in later life.
The under-2s are actually EASIER to travel with than the 4-5 year olds - because you can keep them more confined and closer to you. Normally they're just starting to explore things, and everything is exciting and new on a trip.
We were always in a vehicle and not on a bike - I'd think a bike would make the dangers worse.
If they DO decide to travel, make sure they know that:
- diapers can be hard to find in all but the larger towns. Bring your own!
- it can be difficult to find sunscreen in much of africa, and young kids (particularly but not only white-skinned) burn easily. Bring lots of sunscreen. And if you hire local babysitters, make SURE they understand how to use it. We had a problem in Madagascar where the babysitter claimed to speak french and claimed to understand, but really didn't - so our kids got a bit sunburned (we went scuba diving for the morning).
- they make hiking boots for kids - take advantage of them! Scorpions and spiders are a concern.
- make sure they have int'l medical insurance that includes an evacuation option - hopefully it will be like an umbrella, and bringing it means you never need it.
I tremendously value the experience of travelling to remote places with small kids - even though the kids don't now remember where they were when they were pre-2, I'm convinced it made them more adaptable and more open-minded as they've grown. At the very least, when they were 3-4 and we were reading children's books about rain forests, deserts, jungles and oceans, they had a real sense of what that meant ... And the memories that we have, and have been able to share with them as they've gotten older, are invaluable. I'll never forget my younger daughter, then about 18 months, in a small village in Madagascar staring down the crowd of local kids, and them staring back ... made for a wonderful introduction to their parents!
It's always a personal decision, but I don't think it should be dismissed out of hand. Preparation can take care of a lot.
FWIW.