Looks like the interactivity is running in R Shiny; and I'm hitting "License Quota Reached" errors.
I don't need the R code, but this sounds like it would make good companion data to my own wordfreq [1]. It would be interesting to see which words are learned early but relatively uncommon in corpora, and generally to be able to measure differences in register between child and adult language.
All our code is at http://github.com/langcog/wordbank and you can access the database directly using the wordbankr R package (on cran).
A paper doing something similar to what you describe is in prep, with a conference version here:
http://langcog.stanford.edu/papers_new/braginsky-2016-underr...
we've done some analyses predicting words' learnability from frequency and other factors: http://langcog.stanford.edu/papers_new/braginsky-2016-underr...