The 37-year-old actress shared a photo collage of her son Leo with the 26-year-old singer, her longtime friend and godmother to Leo.
"Wow! @taylorswift13 LT's 1stbday already?! He sends kisses & a bangin' 2 teeth smile to his godmother in Oz. We [love] u!" she wrote.
King shares Leo and 2-year-old son James with director Kyle Newman, whom she married in 2007. The actress named Swift godmother to Leo in March 2015 and explained her decision to E! News the next month.
"I always thought if I were to have another child that she would be the ideal godmother because the way she not only treats me but the way she treats other human beings," King said of Swift.
"She's so loving and giving and so generous and she does everything from her heart and she's incredibly brave and authentic. It's a very rare thing to come across," she added. "I know that [our baby] will always have a very good person and role model through her."
Swift was in Australia with her new beau, actor Tom Hiddleston, over Leo's birthday. King and her family celebrated instead with such stars as actress Nicola Peltz at a cowboy-themed party.
"Happy birthday my beautiful baby Leo Thames! I can't believe you are one today. My [heart] my miracle," King wrote Saturday on Instagram.
King is known for playing Lemon Breeland on The CW series Hart of Dixie, which ended in 2015 after four seasons. The actress will star in and produce the new CW Seed comedy Attention Deficit Theater.