You most certainly can fall pregnant again. I know a few mums that fell pregnant again within 3 months after giving birth. They were fully breast feeding and not trying to fall pregnant. The other mums are spot on, you have to ovulate before you get your period. Breast feeding is about 90% effective as a contraceptive, if you are feeding consistantly and regularly. Having said that, lots of mums get their periods back as early as 6 weeks - others like me, didn't get it back till much later (10 months).
Its funny cause in the beginning I wanted another baby quickly so keen to get my periods. by the time I got them when DD was 10 months, I decided I wanted 2-3 years between kiddies - LOL.
DD is 3yr 8 months - DS is 6 months