I would pay more and use either fedex or dhl. This way you can track its whereabouts during shipment. For the customs description, I would put something like "birthday gift" or "anniversary gift".

Or, if you know anyone that works on the military bases, you could have your friend in the US send it to them.

I wouldn't trust it going through regular US mail to a commercial Qatar address. Maybe letter mail but never something of that value.