No. All inductors don't behave the same way over a range of frequencies. That's why the data sheet specifies the test frequency. Rejoice that it does specify that, some don't and leave you guessing.
The frequency range of an inductor is governed by two things, one is the core material, the other is the winding geometry.
The core material tends to have an upper frequency limit, above which it becomes too lossy to use, the effective permeability often changes as well. This is expressed either as Q, for signal uses, or power dissipation, for power uses. Materials designed for high frequency tend to have lower permeability than those for low frequency, which means that low frequency inductors will be 'better' on other specs, like inductance, and residual resistance.
As the frequency goes up, the self capacitance of the windings can start to turn an inductor into a parallel resonant circuit. The cure for this is to reduce the capcitance by reducing the number of turns, and to use fancy winding techniques that pack less wire into the available space. Again, to make a high frequency capable inductor means sacrificing inductance and series resistance. It is because of the windings issue that even 'air-cored' inductors have frequency limitations.
The specified test frequency will be in the range of 'good' use frequencies. Not necessarily at the top end of the range, it depends what equipment the test house has to hand. For high frequency inductors, the low inductance can mean that Q is very poor at 1kHz, and there is little point measuring at such a low frequency.