Mazal tov on the birth of your baby!
On a halachic level, you are permitted to perform a hefsek taharah, count seven clean days, and immerse as soon as you are able. The restriction for the mother of a girl is not to immerse prior to fourteen days postpartum, which is no longer a relevant restriction in your case.
However, you should be aware that the median duration of postpartum bleeding is three to four weeks. That means that fifty percent of women bleed longer than this. Six weeks (or more) is also common. Postpartum bleeding tends to come and go in waves, so your may well find your bleeding increasing in intensity again. As such, you should feel free to think about mikveh already, but try not to get too invested in its happening immediately. When you are fairly confident that bleeding has stopped is a good time to make a first attempt at the hefsek taharah. For the first cycle postpartum, the moch dachuk may be omitted.