Just about any Catholic song (from the hymnal, for example) will be fine. You don’t need to sing “nursery” songs exclusively.
When my son was an infant and toddler, he never heard the usual baby songs. He grew up with folk songs from around the world (his parents are both musicians), and he’d sing along in his own babyish way.
My friend’s nieces and nephews were singing the Salve Regina before the age of 3
What’s important is that you sing to your precious granddaughter. Sing Bob Dylan; sing songs of the Church season; sing the Beatles; sing Hildegard von Bingen; sing the “Rubber Ducky” song; sing Celtic ballads… Just sing. You will be creating synaptic connections in her growing brain no matter what you sing
But most importantly, you will be creating lifelong memories, treasures that are irreplaceable and beyond value!