Are 1.5"x1.5" poplar legs strong enough to support a 3'x2' hardwood top?

I’m building a mobile (not on wheels) kitchen island for my partner in our new apartment, as a first woodworking project. A 3’x2′ top is about right for the space, and she’d like an overall height of around 37", with a top thickness of around 1"-1.5". I expect to use maple for the top.

Because I don’t have space for power tools I plan on using dimensional lumber, and I planned to use 2x2x36 poplar for the legs. But since that will give me an actual leg width of 1.5×1.5, I’m not sure this will be enough support. I plan to use aprons made with 1×3 poplar, attached to legs with mortise and tenons, along with 1×2 side stretchers near the base of the legs.

Are 1.5" square legs sufficient for a tabletop of this size? And will the use of this thickness of lumber (3/4" aprons and stretchers) prevent a good, solid mortise and tenon joint?