Can I obtain Word2Vec and Doc2Vec matrices to calculate a cosine similarity?
Yes, you could train a Word2Vec or Doc2Vec model on your texts. (Though, your data is a bit small for these algorithms.)
Afterwards, with a Word2Vec model (or some modes of Doc2Vec), you would have word-vectors for all the words in your texts. One simple way to then create a vector for a longer text is to average together all the vectors for the text's individual words. Then, with a vector for each text, you can compare texts by calculating the cosine-similarity of their vectors. 
Alternatively, with a Doc2Vec model, you can either (a) look up the learned doc-vectors for texts that were in the training set; or (b) use infer_vector() to feed in new text, which should be tokenized the same way as the training data, and get a model-compatible vector for that new text.
I am working with text data and at the moment I have put my data into a term document matrix and calculated the TF, term frequency and TF-IDF, term frequency inverse document frequency. From here my matrix looks like:
columns = document names
rownames = words
filled with their TF and TF-IDF scores. 
I have been using the tm package in R for much of my current analysis but to take it further I have started playing around with the gensim library in Python.
Its not clear to me if I have the word embeddings as in the TF and TF-IDF. I am hopeing to use Word2Vec/Doc2Vec and obtain a matrix similar to what I currently have and then calculate the cosine similarity between document. Is this one of the outputs of the models?
I basically have about 6000 documents I want to calculate the cosine similarity between them and then rank these cosine similarity scores.