The G1on is a small multi-effect unit which has guitar effects and amp/speaker simulations.
If you plug that unit into a guitar amp (such as a Fender Frontman), you then have to take into account the voicing of that specific amp - so the amp/speaker simulations in the unit won't actually sound like the amp/speakers that they're meant to simulate. If you plug the unit into a standard PA, the amp/speaker simulations will sound more like Zoom intended them to (may or may not be similar to the device they're trying to simulate...)
In summary; it's your choice. But if you need to buy the new Fender amp, I'd say just use whatever you have at hand until you get more familiar with the unit and the guitar - save yourself some money in the short-term.