Sleeping in crib......

So my LO will be 3 months on the 23rd of this month! She currently sleeps in her bassinet in our room and I’m planning on moving her to her crib in her room around 5 or 6 months! But just the thought of it freaks me out! I’m terrified something is going to happen to her or she’ll cry and I won’t hear her! (Btw there will be a baby monitor in there) I wake up a couple times in the night now just to check her to make sure she’s still breathing! I know it will be good for her to be in her own room but it just scares me to death. Is this normal? Does anyone else feel this way and our afraid to move their baby into their own room? What do you think I should do?