My pregnancies are awful. During my second pregnancy, my husband got a vasectomy- dumb timing, I know, but it made sense for insurance/ work reasons. My son was born still at 32 weeks a week later. We're not complete idiots- we'd even talked about what would happen if one of our kids died, if I lost the baby, etc. and my pregnancies are so awful that I said I couldn't do it again anyway, no matter what. Well, unless you've lost a child, you have no idea what you'll go through afterwards. We eventually determined that there was no way I could get through this without having another. We tried insemination with donor sperm twice, but it totally stressed me out and didn't take those two times so we moved on to a vasectomy reversal. The surgery is very expensive, difficult, time-consuming, and uncomfortable. (It takes hours.) And it doesn't always work. We lucked out in our case and it did work; I'm 25 weeks pregnant now and hoping not to lose this baby.
My point is not to scare you off from a vasectomy- I still think it's the best form of permanent birth control out there. But I'd think hard about doing it while your kids are so young. If your baby died while still nursing, you might go through just what I did- I said I couldn't do it again, but I just had to. There is no way to guess how your feelings will change if you lose a child. I feel like if I lost an older child, having another would not have been such a big part of my healing process because all the baby stuff would have been over with already (though I really can't guess.) The chances seem minute, I know- but please consider waiting until your youngest is at least a year old.