We demonstrate generation of high-power and large-energy noise-like square pulses at 1612 nm in an all-fiber dumbbell-shaped mode-locked Er: Yb co-doped double-clad fiber (EYDF) laser. The custom couplers with high power handling keep the laser function well. Large-mode-area EYDF with high power handling and enough high pump power make it possible to obtain high output power in the oscillator. Compared with figure-eight structure, strictly all-fiber dumbbell-shaped structure without isolator and optimizing splicing loss could reduce intra-cavity loss and improve optical to optical efficiency, which could reduce heat accumulation and enhance the power carrying capacity of EYDF. In order to study the influence of in-band absorption on output wavelength, EYDF1 and EYDF2 with different in-band absorption coefficients are accessed to intracavity, respectively. It is directly demonstrated that regulation of in-band absorption is an effective way to control the output wavelength. Strong in-band absorption could restrain the emission of C-band and make the wavelength range above 1.6 μm obtain enough gain. Linear insertion loss is another important factor to affect the emission wavelength in EYDF fiber laser. At pump power of 8 W, maximum average output power with emission wavelength above 1.6 μm can reach 1.16 W, corresponding to a single pulse energy of 1.26 μJ. SNR of output pulse is 70 dB which indicates the high stability of mode-locking. In order to verify and evaluate influence of insertion loss on the output characteristics of mode-locked laser, a variable attenuator is inserted in experimental setup, allowing us adjust the linear loss of the cavity. By increasing pump power and adjusting PCs, mode-locked pulses could be obtained on the condition of large additional insertion loss. Even though ~ 10 dB additional insertion loss is introduced, the oscillation still could function at 1612 nm and keep stable mode-locked state. This result demonstrates our oscillation could bear strong additional loss and own strong robustness. If excessively large additional insertion loss is added, 1566 nm becomes the central emission wavelength and wavelength component at 1612 nm almost disappears. Our investigation supplies a direct guideline to design high-power fiber laser with emission wavelength above 1.6 μm.