I think you'll need a phono stage and a headphone amp.
I can't think of a headphone amp with a phono stage in it, but then again, they may well exist. Otherwise, your headphone amp will be expecting a line level input, not the minuscule signal from a MC cart.
Edit:
Cambridge Audio duo do the business?
oh.
forget about all that, you have already realised this and found one that does exist - looks fine!
As you have discovered, yes they exist. Probably not as good as individual boxes but convenient. There's all manner of combined magic boxes when you delve into the chi fi brands too.
I think you'll need a phono stage and a headphone amp.
I can't think of a headphone amp with a phono stage in it, but then again, they may well exist. Otherwise, your headphone amp will be expecting a line level input, not the minuscule signal from a MC cart.
Edit:
oh.
forget about all that, you have already realised this and found one that does exist - looks fine!