I am also a single mother, working in the industry. My daughter was much older than yours when I took on a position in a centre where she also attended. She was already 2. There are definite positives and negatives, and issues can arise.
Many centres that allow staff children to be enrolled, prefer that the child is in a separate room from the mother. I have seen children within the same room as their mother, and of course depending on the child, the mother and the dynamics, different situations can arise. I have seen it work fairly well, and I have seen it not work in the best interests for the child, mother and co-educators at all. Some children struggle to 'share' their mother with the other children in the room, the worst case of this I observed was when a kindergarten teacher had her son in the same room as her, and he wouldn't even let her run a group time without clinging to her and screaming.
In another nursery room I worked in, a co-educators baby was in the room. This had worked fairly well until the child became about 15 months old. Behavioural issues began to arise, the mother was reluctant to do a great deal of redirection / behaviour guidance as she felt we needed to do it rather than her to a certain degree. It became awkward for us as co-educators to step in and do this in her mother's presence. There also became issues with one co-educator in particular showing extreme favouritism towards this particular child, which further fueled behavioural issues and caused conflicts of ideas between co-workers as to how we were to guide her behaviour appropriately. In that room, we also had a mother return to work after maternity leave with her young baby. This educator struggled to adequately work with the other children in the room as her attention was absorbed in her own. At times she would prefer to delegate the needs of her baby to co-workers, which at times seemed to be expected to be catered to above and before the needs of the other children in the room.
My daughter settled in to her first child care setting remarkably well, and after a few rough weeks of orientation, absolutely LOVED coming and actually coped better with seeing me coming and going around the centre, without becoming distressed (usually) better than some of the other staff children around her age that had been attending since 6 weeks of age. Issues began to arise for my daughter and I when I became unhappy with how the service was being run (very illegally and horrible practices). Issues with one educator in her room in particular were a major reason that I had to leave that position as I was very upset by how it was handled and how horribly the service was being run in general.
It can also be a fantastic and positive experience to know your child is in the building close by. If you are in a great setting, there are so many benefits for you both, and some services offer staff discounts for their own children. I would just choose very carefully and ensure it's a high quality service, and be prepared that issues may arise.