I can understand your concerns. But, there is no need to panic as there are multiple effective schedules for most vaccines. Meaning thereby, that flexibility in their schedules is unlikely to be of any significant consequence.
1. Regarding HepB vaccine
You can and should give the third dose of HepB vaccine at 6 months age. In fact, the recommended schedule for infants worldwide is 0, 1 & 6 months. The alternate schedules include 0,1 & 3 months or 6, 10 & 14 weeks. So, without worrying about overdose or side effects, you can go ahead and give her the shot.
2. Regarding dT instead of DTaP
Yes, the doctor's observation is correct. The dT or dTaP is for children > 5 years. Basically the small letter 'd' represents a smaller dose of diphtheria toxin for older children.
If your child has inadvertently received the lower dose vaccine, you could consider getting anti-diphtheria titres of your child and decide regarding further course of action.
Hoping that my advice helped clarify your queries.
Dr. Saptharishi L G