Here is my opinion.
Try not to feel guilty hun. I don't think you have anything to feel guilty for at all. Wanting some time away from her, to do adult things like helping with a new business or getting back into the workforce yourself, does not make you a bad mum or even an average mum. It actually makes you a pretty normal mum imo. Having some time apart each week could actually make you a better mum, in that you've got your own time, space, interests etc so have more energy for her when you are together. And it could also show her that you are more than her mum (as she grows up). And like you said, she would probably really love the social interaction.

There is nothing wrong with caring for your own kids full time, but there's also nothing wrong with putting kids into care either. There are advantages to both. Save your guilt for something that actually deserves it!