Childhood anemia affects around 40% of children aged 6-59 months globally and arises from heterogeneous factors, limiting model generalizability. We evaluate a transformer-based tabular foundation model against classical supervised methods under cross-country and data-scarce settings. We used DHS data from 16 countries across Africa, Asia, Latin America, the Caucasus, and the Middle East (n=68,856). We compared Logistic Regression, XGBoost, LightGBM, and TabPFN v2.6. Performance was assessed using AUC-ROC, Brier score, and ECE. Generalization was evaluated using leave-one-country-out (LOCO), reverse-LOCO, and few-shot settings. Subgroup analyses included sex, age, residence, maternal education, and wealth. Feature importance was estimated using SHAP. TabPFN outperformed classical models in low-data regimes (<200 samples), showing higher discrimination and better calibration. Across countries, it achieved the lowest Brier score (0.042) and ECE (0.203). Under full-data settings, AUC-ROC ranged from 0.59-0.76 with small between-model differences ($\leq 0.05$). LOCO performance was stable (0.58-0.69), driven by country context. Reverse-LOCO showed asymmetric transferability. Subgroup performance was consistent with no systematic demographic bias. SHAP identified child age, altitude, and height-for-age z-score as dominant predictors, followed by wealth and maternal education. Performance in childhood anemia prediction is driven more by population variation than model choice. TabPFN provides advantages in low-resource settings through improved discrimination and calibration, highlighting foundation models as promising tools for data-scarce global health prediction.