Just echoing everyone elses words, that what your body is doing right now is perfectly normal, especially this being your first bub.
I'd discuss induction only at the 13th hour, that being just shy of 42 weeks in my mind.
It is very likely your body will initiate labour of its own accord before that anyway, and spontaneous labours are far more likely to progress without the need for interventions which make c/s more likely.
Don't worry, your body is just cooking this bub a little longer!
All the best