Best if you can drive the transformer from a small audio amplifier connected to the output of your signal generator. It will likely have a lower output impedance than the signal generator, so, within limits, the output level will stay constant regardless of load.
Also, the particular style of transformer you linked to will have a relatively poor frequency response because the primary and secondary are side by side rather than one over the top of the other. Really good audio transformers have the primary and secondary divided into a number of layers and interleaved, part primary, part secondary, part primary etc.
And yeah, the output side of the tranny needs to be loaded with a resistor for frequency response tests to make sense. See link regarding impedance ratio vs turns ratio.
https://www.electronics-tutorials.ws/transformer/audio-transformer.html