Our bright, sociable 6 1/2-year-old -- an only child -- has just entered first grade in a public school where she happily attended kindergarten last year.

Now she is waking early every morning, experiencing an anxiety attack and vomiting before she goes off to school on the bus -- a ride she loves.

The teacher says she fits in well at school and shows none of the worry and anxiety we see at home each morning, and the school counselor and the principal say she is doing very well. We know she is receiving personal support at school and is fine while she's there.

Nevertheless, she says that "first grade is too hard," although her work papers are good and I am confident she can manage this academic level. She seems to feel she must be perfect and know all the answers.

Her father and I have told her repeatedly she isn't meant to know everything; that she is learning and, as her teacher also tells her, that it is fine to make mistakes. She still seems overwhelmed by what is expected of her.

Nothing I do stops this anxiety, and we've talked about the issue with her so much that explanations now fall on deaf ears.

My husband feels I have been overindulgent and haven't instilled in her the self-discipline she'll need to handle the obstacles in life. He feels a stricter approach is needed but I don't think a spanking or such will do anything to help her help herself. I am at a loss. Support, ignoring the behavior, threats -- nothing works.

First grade probably isn't too hard for your little girl academically, but it's too hard for her emotionally.

While many children have a tough time making that big switch from kindergarten to first grade, this is more than that.

Your child may be reacting to subtle pressures she feels at home, and you and your husband may need a little counseling to learn to give her the patience and praise she needs, but it's more likely that she should be in junior primary or kindergarten instead of first grade. She is showing the classic signs of the over-placed child.

A child doesn't belong in a certain grade because of her age or her intelligence but because of her maturity. To do well, she has got to be in sync with the atmosphere, so she is eager to get to school, eager to learn, eager to see the other children. The work should be hard enough to be challenging but easy enough to be mastered; interesting enough to be entertaining but repetitive enough to be remembered.

It isn't fair to push a child to the limits of her endurance, nor is it the way to encourage self-discipline. Children learn best when their self-esteem is strong. This is boosted by their achievements, not by failure or fear of failure, and not, of course, by spankings or threats. Pressure will only make your daughter more anxious, teaching her to respond to future obstacles with anxiety, not confidence.

A child may be ready for school if she has achieved 10 of the 12 criteria on this sample from a first grade/reading readiness quiz:

She can recall an eight- to 10-word sentence verbatim; listen attentively for five minutes; count 10 of anything; draw and color and stay within the lines; try to copy numbers and letters on her own; can stand on one foot for five to 10 seconds with her eyes closed; tell her right hand from her left; ride a two-wheeler without training wheels; has lost her first tooth, a criterion required by at least one European school system. She also knows her way around the neighborhood; can tell a policeman where she lives if she's lost and can be without her parents all day without being upset.

She may do all of this perfectly, however, and still not be ready for school if she feels too pressured to enjoy it. And a good measure of enjoyment is what really matters. A love of learning blooms best in an atmosphere of joy.

The child who is over-placed in school will seldom find this joy, even with tutoring. The throwing up this year -- and perhaps bed-wetting and nightmares as well as a short attention span at school -- will, in second grade, turn into dawdling and daydreaming and unfinished work at school. Third grade may bring rebellion at school and headaches and other complaints at home. Fourth grade -- a watershed year -- may be so overwhelming she'll have to repeat it, although this sometimes can be postponed until the sixth grade. Indeed, she may never repeat a grade, but if she's over-placed she will always feel like she's fighting to survive in school and this will haunt her in her career.

Over-placement is described in The Child from 5 to 10, by Drs. Arnold Gesell and Frances L. Ilg, and Louise Bates Ames, PhD. (Harper and Row; $15) -- all of the venerable Gesell Institute.

Your little girl will treat the obstacles of life like stepping stones but only if you lower her grade at school or your expectations at home. Questions may be sent to P.O. Box 15310, Washington, D.C. 20003.

The Young Adult Institute has 36 training films about young children with developmental problems, first shown on WNYE-TV. For a brochure write YAI, 460 W. 34th St., New York, N.Y. l0001.