Erlotinib, Docetaxel, and Carboplatin in Treating Patients With Newly Diagnosed Stage III or Stage IV Ovarian Epithelial, Primary Peritoneal Cavity, or Fallopian Tube Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed ovarian epithelial, primary peritoneal cavity, or fallopian tube cancer * Stage III or IV disease * The following histologic epithelial cell types are allowed: * Serous adenocarcinoma * Mucinous adenocarcinoma * Clear cell adenocarcinoma * Endometrioid adenocarcinoma * Mixed epithelial carcinoma * Undifferentiated carcinoma * Transitional cell carcinoma * Malignant Brenner tumor * Adenocarcinoma not otherwise specified * Must have undergone appropriate surgery for ovarian epithelial, primary peritoneal cavity, or fallopian tube cancer within the past 6 weeks * No borderline ovarian tumor of low malignant potential PATIENT CHARACTERISTICS: Age * 18 and over Performance status * GOG 0-2 Life expectancy * Not specified Hematopoietic * Absolute neutrophil count ≥ 1,500/mm\^3 * Hemoglobin ≥ 8.0 g/dL * Platelet count ≥ 100,000/mm\^3 Hepatic * Bilirubin normal * Meets 1 of the following criteria: * Alkaline phosphatase (AP) normal AND AST or ALT ≤ 5 times upper limit of normal (ULN) * AP ≤ 2.5 times ULN AND AST or ALT ≤ 1.5 times ULN * AP ≤ 5 times ULN AND AST or ALT normal * No hepatic disease that would preclude study participation Renal * Creatinine ≤ 2.0 mg/dL * Creatinine clearance \> 50 mL/min * No renal disease that would preclude study participation Cardiovascular * LVEF ≥ lower limit of normal\* * No poorly controlled arrhythmia * No unstable coronary artery disease * No myocardial infarction within the past year NOTE: \*LVEF evaluation performed only on patients requiring it Other * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for ≥ 3 months after completion of study treatment * No peripheral neuropathy ≥ grade 2 * No other nonmalignant systemic disease that would preclude study participation * No history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80 * No medical, social, or psychosocial factor that would preclude study participation * No psychiatric or addictive disorder that would preclude giving informed consent * No other malignancy within the past 5 years except nonmelanoma skin cancer or carcinoma in situ of the cervix or breast PRIOR CONCURRENT THERAPY: Biologic therapy * No prior immunotherapy for this malignancy Chemotherapy * No prior chemotherapy for this malignancy Endocrine therapy * No prior hormonal therapy for this malignancy Radiotherapy * No prior radiotherapy for this malignancy Surgery * See Disease Characteristics * No planned interval cytoreductive surgery * Second-look surgery allowed Other * More than 1 year since prior experimental or investigational therapy * No concurrent therapeutic anticoagulation with warfarin