Yes this happens and it can certainly end in a perfectly healthy baby. Your hormones are out of whack, but if you've gone 6 weeks and your preg. test is still coming up positive that is a great sign. It means that the progesterone necessary for maintaining the pregnancy until the placenta is formed was sufficient. That's GREAT.
Keep an eye on your diet, especially if you are BFing and make sure you're getting all the nutrients you need. See a lactation consultant with a lot of experience and see a nutritionist who specializes in neonatal nutrition.
It really is OK to get a few periods, espeically in the hormonal chaos of a quick preg. after birthing. The important thing is you did not lose your peanut. If you had, there is no way your tests would still come up positive.
Congratulations!