exoplanet - Could we detect an earth-like planet around another star?

The short answer is no; we cannot quite detect earth-like planets around Sun-like stars with orbital periods of 1 year.

The two main planetary detection techniques are transit photometry and the radial velocity variation technique. Direct imaging of earth-like planets at 1 au from the host star is utterly impossible with current technology - the problem is not the sensitivity, it is the contrast achievable at small angular separations.

The first demands high precision photometry (a transit by an "earth" across a "sun" produces a lightcurve dip of about 0.01%). This kind of precision has been achieved (by space-based observatories), but they have not observed stars for sufficiently long to build up the requisite number of transits (you need at least a few) to confirm a detection at periods of 365 days The Kepler primary mission ceased after about 4 years, meaning it will be tricky to dredge out convincing Earth-like transit signals at periods of 1 year (but not impossible) - and even then you need to perform some sort of follow up to prove it is a planetary mass object, rather than some false positive, and actually estimate the mass to show that it is a rocky planet.

Which brings us to the doppler radial velocity technique. The motion of the Earth-Sun system results in the Sun executing a 1-year orbit around the common centre-of-mass, with an amplitude of about 9 cm/s. This is about a factor of 5-10 smaller than the best precision that is available at any telescope in the word right now.

So - although none have been confirmed yet (there are candidates in the Kepler data), that does not mean that Earth-like planets are uncommon. Indeed most sensible extrapolations of the frequency of Earth-sized planets found at closer orbital distances suggests that they could be quite common (e.g. $sim 25$% Petigura et al. 2013)