Early software size estimation helps to manage software projects ahead of resources, especially in agile methods. Common Software Measurement International Consortium (COSMIC) is an objective functional size measurement standard, evolved to overcome the shortcomings of previous approaches. With the proliferation of agile software industries, large number of requirements are not clearly defined at the early phase of the software development and are left unmeasured, this leads to inaccurate size and effort estimations and in turn failure of software projects. It is also challenging to apply COSMIC in agile developments, this is because COSMIC needs strict formalization of requirements, whereas agile relies on less formal specifications. By exploiting the advantages of COSMIC and agile methods, in this study, we address the problems by developing domain-specific vocabularies for automating COSMIC functional size estimations in agile developments. We employ an experimental research methodology for implementing our proposed approach. We further pretrain a generic BERT model over requirement engineering domain texts and produce a new domain-specific pretrained model called RE-BERT. Using RE-BERT, we develop deep learning classifiers and regressors for COSMIC-based functional process classification and size estimation tasks respectively. The experimental results show that RE-BERT Seq. Classifier provides 78.97% prediction accuracy, which is better among other classifier models (RE-BERT LSTM, RE-BERT Bi-LSTM, BASE BERT LSTM, BASE-BERT BiLSTM, and BASE BERT Seq. Classifier). Overall, RE-BERT-based classifiers provide a 1.40 to 4.80% average improvement over BASE BERT Classifiers. For the size estimation task, RE-BERT MLP provides 0.691 MAE and 0.988 MSE, which is better among other regression models (BASE-BERT MLP, RE-BERT regressor, and BASEBERT regressor). Likewise, RE-BERT-based regressors provide a 1.23 to 3.19% average improvement over BASE BERT regressor models. In general, domain-specific pre-trained models has a promising effect on improving the performance of machine learning or deep learning models towards a particular downstream task in that domain. Keywords: BERT, COSMIC, Functional Size Estimation, Domain-specific Pretraining, Downstream Tasks, RE-BERT, Agile Development