It's safe to run either one on less than 9 volts. You want to try to limit the output power to 5 watts or less. If it's built for 9 volts, then the output power into a 50 ohm dummy load will be close to 5 watts when using a 9 volt supply.
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This is the empirical answer.? For example, on my QMX, wound for 12 volts
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Voltage |? 60m |? 40m |? 20m |? 17m |? 15m
9v???????? | 4.1W | 3.6W | 3.6W | 3.2W | 2.8W
12v?????? | 6.4W | 5.7W | 5.9W | 4.9W | 3.9W
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I would wager that if the QMX is a 12 volt units that you will see somewhere around the 4W range for 9 volts.
Jason