Now we're getting a good discussion! Thanks for the responses.
It is true you can try to out-activate the SSU and force them to commit their troops before you have committed yours. This is the best "counter" I can think of. It's also kind of a bummer, because you either have to game the system and take a lot of artillery spotters, or you have to avoid bringing any of the good/expensive units to the table. Now of course, even this will not work in scenarios where the SSU has considerably more points than you do.
However, even having more activations will not necessarily help you. Even if you CAN out-activate the SSU and force them to commit their copter, there are very few units that can take out a full-health medium flyer in a single round. Sturmkonig can't shoot on round 1, all of the other anti-air walkers can't kill a 'copter in a single shot. Only Grim Reapers/Hvy Recon/Flak can do it in theory, and without sustained fire your odds are pretty bad. So if you try to kill the 'copter and fail, then you've just given the copter an ideal target to nuke in turn 2, or in turn 1 with a carried squad. This is VERY easy for the squad to do if it has Fighting Spirit.
(On that note, I laughed out loud when I read the Advanced Rules for aircraft. They want you to only be able to shoot aircraft if you sustain fire? Really?)
Even so, the above suggestion is still probably the best way to combat the advanced deployment/Yakov combo that I can see, and it's far from a sure thing. This touches on my two biggest complaints about Dust…. the power of having more activations, and the crapshoot that is initiative. Many tourney armies these days use multiple artillery spotters who are there for the sole purpose of providing more activations. Also, initiative is such a crapshoot… going first can sometimes be absolutely critical, and it's either a total roll-off, or your opponent has Yakov and you never get to go first.
I have played a few games with a variant, that you can pass your turn early, before activating every unit. The person who passes first automatically wins initiative for the first turn. So far it has worked beautifully. I seriously doubt the new edition of Dust will incorporate anything like this (or any of the other activation-problem fixes suggested here on these forums) and it's kind of a shame.