Step parent adoption

I know every state is different, but just wanted to hear some stories on how it went and what was done! I got married over the summer and had a perfect little boy! However I have beautiful 5 year old girl, who has my maiden name and no father listed on the birth certificate.. my husband badly wants to adopt her. & she wants the same last name as us.. wondering if any other mamas have a similar situation and any advice with the are parent adoption?!