Advice

So I'll be 40 weeks this Thursday. The baby's head is not engaged and my cervix is high, long and closed. I am scheduled to be induced on Thursday but my doctor said my baby's head is measuring a little big.

She is worried because her head is not lining up with my pelvis & worried it will be difficult to push( I'm only 4'11) I feel like she is hinting toward a scheduled c section.

Should I opt for c section ? Or try the induction ? Anyone had a situation where they weren't dilated at all and baby was big & they were able to have a successful induction that didn't end in c section ?