Maybe I am using incorrect terms. This is not the HD Slimline Dish. It is however the dish which will also bring in local channels.
The old 18" or "round" dish used a 1 1/2" diameter mast. The newer ones as of about a little over a year ago use the same 2" mast the current HD (Ka/Ku "Slimline") dish uses.
Very likely your mount is the old one, so yes, you'd need a new mast installed.
New dish will most likely go where old one went. New one will have a larger foot plate for mounting. As an installer I usually remove the mast and old dish. I leave the old foot plate. I mount new mast. The old foot plate remains so there is no leaking from damage to roof while removing it. Sometimes It can be removed, but if a lot of sealer was used it does more damage to remove plate than to just leave it and take off the old mast. Directv has a new mount for the KaKu slimline. it is about a foot tall and does not need the monopoles. Each installation will vary and yours may or may not be able to use this mast. Discuss it with your installer and see if he has and can install the new mount. This new mount isn't for every situation, but yours could qualify. The installer will let you know and if he has one can put one up for you. They really look nice and I try to use them as often as I can.
Do you have a link or pic of that new mount? How would that one do in a hurricane vrs the typical Plate/mast style?
The mount would be fine in a hurricane, just as the mount of the old style would be.
If you know a hurricane is coming, take the Reflector off (4 bolts) and you'll more than likely be fine, when its past, bolt the reflector back on and your good to go, If you have power that is.
That's what I did last year when Irene came through. It's the only time in six years that I took it down, IIRC.