This is a perfectly reasonable concern, however I think the specification of the unit allows for it, so I would be quite happy with my recommendations.Mr. Rusty's words are true, but I have some concerns that consumer grade portable voltage convertors may be stressed by the high inrush currents that the flash electronics suck in right after the flash has be triggered.
Holly - Consult a local electrician for confirmation, but apart from the cost :-( once you have the correct step-down everything will work fine.
Mike - The tech data (for the CE 230V unit) shows it is fused/rated at 6.3A for 1500VA (6.3 x 230 = 1449). For some reason they don't quote the fuse rating for the 120V unit, but assuming the overall power consumption is similar (I think it might be a little lower as the bulb rating is slightly lower), the 1500W rating is actually the maximum connection load including any surge - if it wasn't the fuse would be underated! I expect that the actual draw is quite a bit below the specified rating. For this reason I would be quite happy with the 1500W step-down I provided a link for as it is rated continuous 1000W and up to 1 hour continuous at 1500W. I expect it has a current limiter/fuse set a bit beyond that.