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.