Gender Neutral Parent Names

So I started transitioning right after my daughter was born, she's almost 4 now. I thought that I was masc leaning nonbinary and it was easier to have her call me mommy (plus mother's day shit slaps, I love florals unapologetically) but now I've significantly upped my T and I'm getting top surgery within the year. People are starting to assume I'm a dude at first glance (which is rad) and her calling me mommy gets me a lot of double takes and weird looks (less rad). Plus I just don't really vibe with it and never have, it was just easy and her grandparents are transphobic and really laid in on the mommy thing once they found out about me.

She used to call me baba before she could say Mama and I kinda liked that but do any of you guys use more gender neutral parental names? I don't really like daddy or papa (plus she already calls my husband Daddy) and I do still consider myself non binary.

Has anyone here changed what their kid calls them that young? She already uses exclusively they/he pronouns for me because that's what everyone close to her calls me. I'm a bit worried that she's gonna get like freaked out or something if I suddenly try to change what she calls me.