Hi, Julie!
Your granddaughter is one lucky little princess to get to go Walt Disney World with her grandma and grandpa!
February until the week after Easter in April are going to be fairly busy with Spring Breaks, all which seem to fall at different times keep WDW busy throughout the spring. The busiest weeks will be the week of President's Day in February, 3rd and 4th week of March, and the week before Easter and the week after Easter. I would probably aim for the last week in February, or if you can wait (and will have better weather) plan for end of April.
You will want to keep checking
HERE for the latest Special Offers. There is a great deal being offered now for Free Dining (for arrivals through March 7).
You will also want to check airfare to see when you can get the best rates on your plane tickets, as that may factor in your decision on travel dates.
Have fun planning! Once you choose your travel dates and resort, let us know if you need some ideas for dining, tickets, or any other planning needs. Have fun getting ready for your magcial vacation!