Can I breastfeed my baby and my toddler at the same time?

Yes. As long as you make absolutely sure the younger baby gets enough. That's the priority; breast milk is dessert to a toddler, but main course for an infant.
Yes. A mom can breastfeed a toddler and a new baby. Just be sure the toddler is not aggressively defending his food supply. In parts of the world where children are spaced closely together, and where there isn't ample baby formulas, mom's are more likely to breastfeed both a toddler and a baby. In america, a toddler may be persuaded to eat "big kid's" food and milk, leaving the breastmilk for baby.