BF a natural BC

FTM here, my Dr said that because I'm EBF that it's a natural BC. I'd like to try for a vbac when the time comes and we're ready for baby #2. My question is how many of you BF momma's did not use BC and just used the pull out method. My husband and I don't use condoms because I'm allergic to the latex and it can cause some pretty uncomfortable utis. The goal is to wait at least 2 years before we try for baby #2 so we can attempt to have a vbac (we planned to do a natural water birth with midwives but due to my body going 42 weeks and not wanting to cooperate by going into labor naturally and even with being medically induced I had an emergency c section). But regardless the Dr who delivered my baby said to wait a year (she was under the Impression I wasn't going to try for vbac). I guess my question is is bf really a natural BC or did any of you ladies still get pregnant while EBF? Also how soon is it safe to get pregnant again? I'm so scared I see so many momma's on my different mom pages getting pregnant right away after having a baby! I really would like to give my body time to heal before having another one.