Passport for a new born baby in Khobar

I live in Khobar and Allah has blessed us with a baby girl 2 weeks back. I already have got her birth certificate from Ahwal Madina... Problem is I want to travel back to Pakistan next month... but the duration to get the electronic passport is quite long. My question is.. what if I get the manual passport of my baby from Riyadh and travel to Pakistan... and then get the electronic Passport from Pakistan? Will my baby be able to travel back to Saudi again on electronic passport.. considering she will not have Iqama, because what I have heared is.. Iqama is only issued on electronic passport...just know how will that work?

Thanks