Sorry for the long reply- but I have recent experience with this.My DD was similar - right hip fine but left slightly too shallow. She had the Pavlik harness fitted at 3 week old for 10 weeks (they initially estimated she'd have to wear it for 12 weeks but a scan at 10 weeks showed the harness had corrected it)
She was a bit fussy for the first 24 hours whilst she got used to not being able to move her legs but after that was totally fine.
We weren't allowed to remove it at home but went to the hospital every 2 weeks where the physiotherapist removed it so we could bath her. Other than that, we topped and tailed her every day and used a washcloth to wash around the harness. There were certain straps you could undo to clean under but certain ones you couldn't (physiotherapist should cover this with you)
Clothes wise, sleepsuits and vests are totally fine - we just went up a size to fit over the harness but if your DDs current size is a bit loose it should be fine. Dresses with tights and rompers suits are also fine (again we went up a size) Normal leggings won't fit over it but Marks and Spencer do a special range of clothes for hip dysplacia - with leggings that fit over it. (We didn't bother with this as it was summer so she just lived in dresses)
DD is now 10 months old and has had no further issues. She's still to get her follow up scan when she turns 1 just to check it.
It was a bit of a shock for us as we first seen her in the harness but honestly she was totally fine the following morning. Took us a couple of days to get used to it too, having to adapt nappy changes etc slightly.
I hope you have a similar experience to us and that your daughters hip heals quickly! If you've any other questions just let me know 