Working while in iddat

I am 31 years old and been married for 7 years. From the first day my husband was unable to consummate the marriage because of his mild autism and anxiety issues (his father was very strict and abusive which according to doctors have resulted in his personality disorder). I tried to resolve the issue with the help of psychiatrists and urologists. He was barely able to perform under very high doses of medicines. He never came near to me until I requested him that we have to do intercoarse for having kids. Otherwise, It happened several times that we lived without intercoarse for 9 months to 1 year.

Later on I came to find out that if he does perform he still can't become a father because he is infertile too (with great difficulty and several attemps at clinic, he was enabled to deposit semen for test).

Now I have decided to take the divorce as I am tired of this nursing and unfulfilling life. For about a year we have never come closer. We practically sleep and live in different bedrooms.

My question is, if he agrees to sign the divorce papers, do I have to complete the time of iddat? My periods are fine and regular and it is very clear that I am not pregnant.

Secondly, I work as a research officer in a university which won't give me leave for three months. It is very important for me as I am financially dependent on this job. Moreover, can sit in iddat (without marrying another person) while going out of the house to work?