I wouldn’t worry about the specific font-sizing in pixels because pixel sizing really makes a site non-responsive because a pixel isn’t responsive - it’s a fixed measurement.
I don’t recall the thread (edit: it’s this one), but Paul (our resident CSS guru/jedi/master) makes a good case that pixels are best for margins/paddings, but for the rest of the measurements should be in percentages (for height/width) or in em/rem (for font sizes/line heights). There are also viewport relatives (vh, vw) but are harder to master.
Did your “designer” give you a small device design, or did they only give you a desktop version?