Another apprach: using the Boost Date_Time library:
library(RcppBDT)
dates <- seq(as.Date("2010-01-01"), as.Date("2015-12-31"), by="1 month")
do.call(c, lapply(dates-1, getFirstDayOfWeekAfter, dow=Mon))
# [1] "2010-01-04" "2010-02-01" "2010-03-01" "2010-04-05" "2010-05-03"...