Most frequency counters have a period mode, which will measure low frequencies like your 1Hz output to about 0.1ppm
Bear in mind a 'vanilla' frequency counter will have a crystal timebase, likely to be accurate to maybe 10ppm.
A TCXO based one will be down to a few ppm, and an ovened osc maybe below 1ppm.
Or get one of the various cheap rubidium reference oscs and use that as a reference ( any decent counter will have an external reference input)
For a single-task test type application, a cheaper option would me a micro clocked from one of the accurate sources above would do the job pretty easily.