Hello Cheila and thanks for bringing such a great question to the Disney Parks Moms Panel.
I can't think of a more magical place other than Walt Disney World Resort in which to celebrate your darling little Mouseketeers 1st birthday in! It truly is practically perfect in every way.
Although at present I don't believe there are any discounts on 1-day Magic Kingdom Theme Park Ticket it is certainly possible to purchase 1-day
Disney Theme Parks Tickets.
However, I'm super happy to share these current
Special Offers, Deals and Discounts in which you may find something to suit your families needs to visit Walt Disney World Resort.
In addition and specifically for
Florida residents there are some other wonderful current offers found here in
Florida Resident Tickets & Passes which does presently include a 1 day Ticket with Park Hopper Option.
Plus I also thought it might be helpful for you to know that there are
Baby Care Centres in each Disney Theme Park; Baby Care Centres provide a calm oasis in which to feed, change or nurse your little one.
Wishing you and your lovely son a very happy 1st birthday visit to Walt Disney World Resort.
Have a great Disney day.
~ Jane