Here's a suggestion...
You'll have to be pretty aggressive to level out the damage. I would try a 3M rubbing compound that's safe for clearcoat and a direct drive buffer, like the Makita 9227c. The buffer can be had for about $200.00, likely about the same a detailer will charge you to take the damage out.
If you decide to go this route, use foam waffle pads, not lamb's wool. The lamb's wool pads heat up more quickly and will burn your paint in a heartbeat. The foam waffles are a bit more forgiving for an amateur. The 3M compound will leave swirl marks, so then you'll have to go through the whole rest of the routine to get back to pre-duck. Be careful, take your time, keep the RPMs down and you can fix it yourself.