How often do you bath her?
Small babies don't need bathing everyday, once a week is absolutely plenty and topping and tailing will keep her clean.
With DS1 we fell for the 'bath every night as part of the bedtime routine' and his skin became very very dry as we were washing away all his natural oils.
Once we reduced the baths to once a week his skin cleared up and there's been no sign of eczema since (he's 7 now).
DS2 has 'proper' eczema, despite only ever being bathed once a week. I can't remember when it first flared up (6 months ish?) but it's definitely an allergy rather than something I've done.
If eczema runs in the family then she does have a higher risk of developing it, as you know, so if she has it isn't your fault.
However, there are things you can do to minimise the symptoms.
As few baths as possible in plain water only - all of the additives don't really do anything to help and in ds2 cause extra allergic reaction because they are full of chemicals.
We cover him in moisturiser before he goes in the bath and then pat him dry very gently when he gets out. We then cover him in moisturiser again once he's dry.
Personally I love Pure Potions Skin Salvation as it's completely natural and has no chemicals in. We tried all of the emollients available from the GP but they all made it worse so we assume there's a common ingredient that he's allergic to.
When it's bad we moisturise the sore bits morning and night, if he's okay I do it every night before bed. The softer and moister you can keep the skin the better where eczema is concerned.
HTH