How do you age up your newborn into a toddler with a birthday cake?

Pick up the baby and click on the cake. You will have a list of names to age up, choose the baby.

Please?

I don't; I use NRaas MasterController to trigger the age transition. But building on what @Simasaurus09 says, select a teen/YA/A/Elder, pick up the infant, then click on the cake.

It's the same with toddlers, by the way, since they can't reach the table to blow out the candles for their toddler to child birthday all by themselves. :)

The Sim holding the baby blows out the candles and 'helps' the toddler blow out the candles.