Hi A.,
Most health experts recommend waiting until a baby is six months old before introducing solids. There are several compelling reasons for this. First, a baby's digestive system is not equipped to break down proteins until then. ***Note: even if the baby seems okay with the solids now, problems may arise later--there are some studies that link adult GI problems to early introduction of solids. Also, giving solids (particularly iron-enriched cereals) too early can reduce efficiency of iron absorption later on. Additionally, introducing solids too early may cause obesity as well!!! (That anyone would want to put their child at risk for a lifetime of weight problems because they can't wait a few months really surprises me...) (See for example: http://www.kellymom.com/nutrition/solids/delay-solids.html.)
Also, remember that babies are often fussy for reasons unrelated to hunger. All too often we want to shove bottles or food in their mouths to quiet them when it isn't necessary. There is a myth floating out there that putting cereal in formula will calm a baby, make him/her sleep longer, etc. However, there is no evidence whatsoever to support this. (See, for example: http://www.babycenter.com/404_will-my-baby-sleep-better-i...) How old is your baby? What else have you tried to ease the fussiness? Are you using a pacifier? Sometimes babies appear hungry but really just need something to satisfy their "sucking reflex." What about music, rocking, swaddling, swinging, etc.? (On a few rough nights we resorted to putting our baby in the bathroom in a swing with the bathroom fan on ("white noise.")--worked like a charm.) Dr. Karp's "Happiest Baby on the Block" DVD was helpful.)
In short, there is no reason to introduce solids to your child before six months (unless of course your doctor recommends it w/some medical rationale.) It's unhealthy and doesn't work anyway. If you feel you feel like your baby is excessively crying or fussy, you might want to take her in to see the doctor to see if there is an underlying medical issue. My son was diagnosed with reflux early on and Zantac worked wonders.
I hope that helps! Good luck!