You should give yourself a day to recover, even when doing bodyweight exercises (assuming that you're going to start adding weight as you get stronger!) Muscles grow and get stronger in *recovery* from weight lifting, not from weight lifting itself, so don't cheat yourself from your day off.
If you wanted to work out every day, you could alternate upper and lower body days: Like on MWF do squats, deadlifts, lunges and step ups, and TThS do your push ups, presses, planks, ab work and etc.
"Losing weight is easy; I've done it dozens of times."
(with apologies to Mark Twain).
Ultimate goal: Size 10 clothing.