She's very young and tiny! It may be too soon to get her to go outside. I agree that you should check with your vet to see if she's ready to be outside with other doggie 'stuff.' Given her size, I don't think you want to over stress her either.
My Lucy is 6 months & 5 lbs and she's been going outside like a dream! I didn't crate train (but was prepared to do that if needed.) I kept her limited to an ex-pen while I was not near her. Now, she's restricted to my kitchen while I'm away. She's finally to the point where I can leave her on her own for several hours while I go to work.
I think your baby may take longer if she remains a tiny. It also may be awhile before you can leave her alone for periods of time.
You may need some better advice from YT members who raised tiny ones.
Good luck! Enjoy her.
Tracey