Is Della pregnant?

There is nothing in "The Gift of the Magi" that makes explicit that Della is pregnant. In fact, the narrator describes her as "quite thin." Granted, it is not impossible that Della is expecting a baby, because she could simply be in the early weeks of pregnancy. But given the economic circumstances of the young couple, it is reasonable to assume that they are not actively planning to have a child at this time.
Though some readers may read the narrator's observation of Jim's situation (e.g., "Poor fellow, he was only twenty-two—and with a family to take care of!") as an oblique reference to Della being pregnant, that is not necessarily the case. When Jim and Della married, they became a family. The narrator's exclamation could also mean that Jim had financial obligations to members of his own family.
Another reason that a pregnancy seems unlikely is the nature of the gifts that Jim and Della exchange. If Della were pregnant, buying Jim a gold watch chain would be highly impractical. Likewise, Jim buying his wife a pair of fancy hair ornaments would be impractical with another mouth to feed on its way. Though they are young, the couple seem too thrift-minded to throw money away on luxurious gifts if they know their budget will soon be stretched even further when the child arrives.

And when they were come into the house, they saw the young child with Mary his mother, and fell down, and worshipped him: and when they had opened their treasures, they presented unto him gifts; gold, and frankincense, and myrrh. Matthew 2
“The Gift of the Magi” is perhaps O. Henry’s most popular story, and as such, it has been the subject of much critical analysis. One line of thinking examines the story's title and the links to the three Magi in the story of the birth of Jesus. The Magi are not only rich but they are kings. Della and Jim are barely getting by on twenty dollars a week. The three kings give valuable presents, including gold. Jim has to sacrifice his watch and Della her hair to buy simple Christmas presents. The Magi in the New Testament do not give presents to each other. Most significantly, the Magi bring gifts to a newborn baby. But there is no baby in O. Henry’s story.
Or is there?
The general interpretation of the story suggests that the gift of the Magi that O. Henry's title alludes to is simply Jim and Della's spiritual enlightenment in realizing that their love was more important than material possessions. But O. Henry gives an interesting hint that the common denominator between the two stories might be a baby. Here is the one significant passage:
The door opened and Jim stepped in and closed it. He looked thin and very serious. Poor fellow, he was only twenty-two—and to be burdened with a family!
Della does not think Jim is burdened with a wife but is to be burdened with a family. Might Della be expecting a baby?