I read this book and I thought it was good.
https://www.amazon.com/Becoming-Vegan-Express-Plant-based-Nutrition/dp/1570672954
It has a specific chapter on children including a section for toddlers but the whole book about vegan nutrition is useful.
When you read generic articles on vegan nutrition, consider that low protein, low calcium and perhaps low fat as mentioned above may be more risky for children than adults. So possibly do extra research on these topics than you would for an adult to check whether or not I'm right. And be skeptical of claims that vegans can eat very low protein or low fat. Such claims are not necessarily meant to be applied to children.
However there is a strong and growing body of evidence, in terms of lack of reported problems, scienfitic studies, and examples of healthy vegan children, that the odds of deficiencies and growth problems for children with a well-planned vegan diet is probably very low.
I can't give specific advice for 1 year olds, though. In general, I think healthy vegan diets are possible for all and it's true that the needs of children and adults are pretty similar. However it's also true that the younger the child I think the more there is a need to be extra careful and get specific advice and likewise the less likely that non professionals are going to risk giving advice.
I hope you manage to read the above book and get an appointment with a nutrionist. If you have done both things you will also be able more easily to defend the diet to concerned others.
From an ethical perspective advice might be to go vegan immediately but from a health perspective I suggest you remove foods one at a time and add foods one at a time, and perhaps slowly, and keep an eye out for any changes or reactions.
I can say that I personally have no experience with children on a vegan diet at all so keep that in mind.