Looking at the Wiki, it suggests I get NCR infamy if I get the BoS to sign the peace treaty. I don't want to lose any standing with the NCR in this play through. But if I take out the BoS, I lose Veronica. What's the deal?
As above said, Moore wants to see them gone, they are enemies of the NCR after all and you were given orders to kill them. You can facilitate a peaceful arrangement but it's going against their orders (to them you're simply a highly skilled civilian contractor). The karma drop is not enough to drop you a level, assuming you've done nothing else to annoy them (even something small may be enough to drop it)
As for Veronica, well, you did just kill her family and friends, even if she grew apart from them she still loves them, murdering them all would make her pretty angry. I think it is possible for her to remain a companion IF you convince her to join the FotA during her quests, she gives you a last warning and is pretty peeved but doesn't leave...