Yes it is safe for You to clean and mop the floor
You can clean your house just avoid the harmful chemicals such as triclosan, which is found in certain antibacterial soaps and other household products and nitrobenzene, which is in some furniture polishes. Pregnant women can limit their exposure to chemical cleaners by wearing a mask (so as not to breathe in fumes) and plastic gloves while cleaning – a good idea even when not pregnant. If weather permits, keep windows open while cleaning for good ventilation; if you can’t open a window, use a fan, especially when cleaning bathrooms and other small spaces. (Needless to say, a supportive partner who pitches in with the cleaning is also a big help!)
Houseplants can be a valuable assistant in the cleaning process; during their natural “breathing” process plants absorb chemicals from the air and help clean the air in your home environment. Bear in mind, though, particularly if there are already small children in the house, that some houseplants can be poisonous if ingested
Read more: http://www.justmommies.com/articles/cleaning-products-pregnancy.