Mazal tov on the birth of your baby!
We do not recommend delaying immersion until after the insertion. There is often staining associated with IUD insertion, which is easier to handle halachically after mikveh. (For more details on staining, please see our articles on Stains and Toilet Paper.)
We suggest you discuss the situation with your health care provider to make the decision that is best for you. One possibility would be to immerse to enable other forms of closeness, but to delay having relations until the IUD is in place. Another option would be to use spermicide as contraceptive, which should be sufficiently effective at this stage postpartum, especially since an IUD inserted within four days of relations is itself a form of "morning after" contraception.
Please write back with any further questions.