This is not one of those questions which can be answered with guarantee. Usually it depends upon the speed of the illustrator and also at times, on the deadline of the Author, who wants to publish a book by a certain month of that year. I have generally seen that if the Author and the illustrator are at the same frequency, then everything remains good and the book is illustrated in time but at times when there is communication gap or there is a gap between the illustrator’s abilities and desired quality,the things can be very challenging.
The Author must spend time in selecting the illustration style / styles which he/she wants for the book and ask the illustrator to provide a paid sample in order to be sure of the capability of the illustrator. Following your feelings without actually checking children book artists work may damage your plans of getting a great book.
Children’s book success is result of a typical trio , the story line, illustrations and the marketing effort. If there is anything which is lacking, it must be improved upon and rectified in time. If you get a feel that illustrations are not coming out nicely, please talk to the illustrator and solve the issue before the book is completed. If you make the same effort after the book is complete then you will end up wasting that much more extra time. In the same manner, the story line should be such that it can hold a child’s attention through out the story, it may be simple, yet exciting to a child. It should not be something which a child is not able to enjoy. For this, get your story reviewed by others, may be friends, other authors from some authors community etc. Marketing effort should be planned well in advance and all the effort which is required must be made here and if possible, also get an e-book version of the book because parents and kids are preferring to buy ebook now a days more than the printed books.
Any children book from its inception of the idea to publishing can be done in 8-10 months, if the Author is well planned and may take 3-5 years If things are allowed to move at its own pace. There is nothing wrong in taking more time for publishing, the only point is that if we can save time, we must do that.