LEAD: THIS television season has been filled with images of single professional women thinking about having children on their own: Melissa, the spiky-haired photographer of ''Thirtysomething,'' considered it. So did Murphy, the egotistical television journalist of ''Murphy Brown.'' J. C., the successful executive of ''Baby Boom,'' has been raising a child on her own, and it looks pretty much of a snap.

THIS television season has been filled with images of single professional women thinking about having children on their own: Melissa, the spiky-haired photographer of ''Thirtysomething,'' considered it. So did Murphy, the egotistical television journalist of ''Murphy Brown.'' J. C., the successful executive of ''Baby Boom,'' has been raising a child on her own, and it looks pretty much of a snap.

For the single professional women in their 30's and 40's who have chosen to bear and raise children on their own, the reality is a lot more complicated. And precarious: so much hinges on dependable child-care arrangements, and on the emotional and sometimes financial support of family and friends.

But many women who are able to manage all this describe themselves as more fulfilled than they expected to be; they are rapturous about their children. A dozen of them - self-supporting middle-class women around the nation earning $22,000 to $50,000 a year - said in interviews that they knew what they were getting into, despite the romanticized television images, and that they were surprised at how little prejudice they encountered. They expressed no regrets about their choices, though most were wary of recommending single motherhood to others.

The number of older single mothers is increasing. The National Center for Health Statistics of the Department of Health and Human Services said that of the 3,756,547 live births in the United States in 1986, 106,492 were to single women in their 30's and 40's; in 1985 there were 3,760,561 births, of which 95,477 were to single women in their 30's and 40's.

''There's a significant minority of women choosing motherhood at an age when they can't stand around waiting for the perfect relationship,'' said Judith Walkowitz, a professor of history at Rutgers University. ''They're aware of the high divorce rate, and of the instability of marriage as an institution. These women have the financial resources to make this decision, and they feel it's not such a deviant position. They won't look so different from divorced mothers.''

Here are profiles of three of the women interviewed for this article. NORA LEE, a 38-year-old teacher of children with learning disabilities, lives in Brooklyn, has been divorced twice and was told by doctors that she was infertile. She was delighted when she learned she was pregnant. ''There was no way I was going to have an abortion,'' she said. ''After all these years?''

Her pregnancy...