A bun in the oven

Meaning

Pregnant. Oven = womb, baby = bun.

Origin

The allusion may just be to the loose connection between 'baby' and 'bunny'. It's more likely that this, and other terms for pregnant, like 'up the duff' and 'in the pudding club', all share the same euphemistic source.

The phrase is 20th century. The first citation I can find is in Nicholas Monsarrat's Cruel Sea, 1951:

"'I bet you left a bun in the oven, both of you,' said Bennett thickly... Lockhart explained ... the reference to pregnancy."