Hello Charlotte!
I think that you should plan for at least one week at Disney World. The first thing I would do if I were you, would be to visit the
Disney Parks pages and look through all of the attractions offered in each park. Once you decide which things are on your "must do" list, you may have a better idea of how long your stay at Disney World should be. I would also try to decide which restaurants you might like to visit, as that may help you decide on your length of stay as well.
I personally believe that the longer you can stay, the better. It is much more fun to be relaxed and take your time enjoying the parks, than it is to rush around trying to fit everything you want to see into a few days. If you would like to visit any of the water parks or Downtown Disney, it is important to account for that when planning how many days you will spend.
I have traveled to Disney when my daughter was 2 1/2 and you definitely have to factor in time for breaks and naps. Touring the parks should be more relaxed when you have young children with you, so they don't get overwhelmed and cranky! It makes for a much more enjoyable experience when everyone is rested and having a good time instead of feeling tired and stressed.
To answer your second question - yes, you can absolutely book a night at a Disney resort before you begin your package. You will need to make a separate "room-only" reservation for that first night. When you call to book your package, the cast member will also be able to do this for you.
I hope this helps you plan your stay at Disney World. have a wonderful time!