Try using one of the baby's parents. Click the gender icon, not an age icon (I think by default the dialogue will pop up with the age of the selected non-infant Sim showing, but I'm not sure) as soon as the window to buy clothing pops up. Clicking a gender icon instead of an age icon (do NOT click an age icon) will get you your baby clothes. Add them to your cart and buy them normally.

If your game is crashing somewhere in that process, I'd guess you have either a mod conflict or a deeper problem I don't know how to fix.