Most days she is napping 1.5hrs total in a 12hr period...I mean, that's just crazy.
Would you think that if you hadn't read any books or routines? Sometimes it's the expectations we have that hold us back from accepting what is.
Don't feel badly about doing stuff in her A time. I often did (and still do) a lot of housework during my LOs A time. They really are ok playing on their own. She gets lots of love, hugs and cuddles from you at other times. If you're still feeling uneasy about it look up RIE (Resources for Infant Educarers) - the whole premise is that LOs are ok to play on their own even as babies - they get the stimulation they need at feeding, bath and nap/bedtime rituals.
One book I read gave 1-2 hours as the A time guidelines for 0-4 months. I find reading that made me a bit more flexible in how I thought about A times at that age. Maybe a longer A time might help her get a better first nap?