Is the noise/feel at the 1 min point or more like when you reach about 10 mph..? Do a search here in the forum on "ABS check".
Basically, the car performs a quick ABS ops check each time you drive off after the car has been sitting for an amount of time. You tend to feel it in the gas peddle etc. as well as hear it.
Hopefully that is all you are experiencing. Perform a forum search. You will find a bunch of others who have asked the same question... Even me

 

I also have an 05 and I have been very happy with the car. I have just over 1200 miles and have also noticed this vibration issue. It happens once in a blue moon on my car. I personally think it has something to do with the tires or rims but the best thing to do is leave it up to the professionals. I am sure they are aware of the problem and they are working hard to find a solution. To them it is like finding a cure for a disease, they will find it, but it may take some time. Check with your local Acura dealer every so often to see if they have has any breakthroughs with the problem. It is difficult to understand how problems like this arise on a $35K car, but it happens! Look at Mercedes, they have the worst customer satisfaction out of any manufacturer. They recently recalled a million cars for electrical problems!!

 

Update: I brought my car to the dealer last week. The vibration issue was caused by my tires not being properly balanced by the dealer’s crappy non-Hunter balancing machine. My dealer had to send my tires to a dealership that had a Hunter balancing machine to get the tires properly balanced. Problem fixed. My dealer told me that they might look into purchasing a Hunter balancing machine since they have had several complaints.