I have done it, but it's exhausting. My kids are 18 months apart, and I did take them to the zoo on my own and the aquarium on my own, but I enjoyed the experience a lot more when Hubby could come along.
Make sure you have a carrier for the infant (I prefer the Beco, but I know lots of people swear by their Ergos, too) which should help with the nursing, again. Bring a stroller for the toddler so that, if things start to become overwhelming, you can strap the bigger one down for a bit. Pack your diaper bag the night before so that you can put anything you forgot in the next morning. It can be done! But remember, you don't have to!
Good luck!