Pursuing this might not be totally impossible, but you should probably have a sit down and really contemplate the effort you will need to put into this. For starters, depending on the age of your child, you're going to need diapers, clothes, food, entertainment, a decent sized trailer, all of your regular touring gear, and extra emergency equipment such as first aid, bike maintenance, and child care.
Beyond the massive load you're going to have, you should also consider how your child will react to all that time spent in such a small space. If you need to bring toys/books/electronics with you, that will add to your over all weight, as well as bringing up the fact that if you are bringing electronically devices for them, how will you charge them? A bike battery pack is expensive, as well as adding more weight to your load.
Depending on how old the child is, you will quickly find out how many times you are going to have to stop and care for the child. A ride that takes you a few hours by yourself could easily take you all day, or even longer, when your child is with you. Not to mention carrying all of your supplies.
Prepare for any kind of weather.
Have an emergency plan in case of, (and I hate to bring it up), any accidents on the road, bike malfunction, possible outdoor area hazards, e.t.c.
The list goes on and on, but the basic fact is that it will not be nearly as easy as you think it will be. I would suggest taking your child on test rides and see how things go. And, being a toddler, you have to take into account that the longer they are in the trailer, the less they will want to be in it. With all the hassle of your load, the traveling, and a very grumpy toddler, the trip could turn into more than you bargained for in the blink of an eye.