How do you give birth to a pup when your females a higher level than your male?

It doesn't matter if the female is a higher level than the male, or if the male is a higher level than the female, as long as they're 10+ they can have their first pup/cub/kitten.

In your 'Family' tab, there should be an icon with a + inside a circle. Tapping on this will tell you what level both animals need to be to have their next child.

Once both animals are at the appropriate level, all you need to do is have them both sleep inside your den. Then level up the female, who should be pregnant when they wake up.

When the female is ready to give birth, a message will pop up on your screen indicating this. It's pretty hard to miss as it won't let you do anything else until you dismiss the message. Then, you just go to sleep in the den again and viola! The abridged miracle of birth!