Well quite a few people will come in here saying Focus attack it to break the shield or stop her from casting in the first place or any other aount of unhelpful advice. The only thing you can really do is:

A: hope you have a high enough DPS that you can focus HER and kill her shield and her. Trying to take on her allies with her shielding is a losing battle.

B: GTFO. scatter, make them split up. Go contest their flags in other places. Back up to your towers. Hide.

Basicaly, though it is sad, from what I have seen if you have 3 live players, one being a good QoT and the other 2 know how to play WITH a QoT, not much is going to stand in there way. Now an equal combo, such as sednas heal on your side will even things out, but short of that or something else equal to the bramble shield, your going to have an extremely tuff time.

I wish there was more mana burn items for this exact reason.

What Demigod do you think would be best against the constant shielding strat?

It depends - If QoT has an ally with more survivability than her (i.e. a Tank Rook, a Heal Sedna) then focus your damage on her - the shield will overload eventually and then she crumples.  If QoT is allied with someone like a DPS Reg or TB then focus on them, after they are dead you can sweep her up. 

If she kites like she should then you have to get close and deliver overwhelming damage after the shield comes down.  Use regular attacks on the shield and save your nukes for actual hitpoints....Speed items, slows, and blink items like Cloak of Night and Warpstone will keep you close enough to take her down or at least out of the fight...

QoT is beautiful on kite teams but I'd say they are also her weakness.  Her most effective counter would probably be a DPS/Slow/Mines Regulus

The cooldown is unfortunately very short. 7s I believe. If you have 2 or 3 high dps chars on your side you can indeed break the shield and kill her before she can raise it again. There is also the abilities that increase cooldown. Those can help but again it really relies on having a large amount of good DPS.

Yuo are corrcet however that focusing on shield skill and items to perma shield you and your allies does reduce her offesnsive effectiveness. The main thing here is this is one of those strategies that dominate when the skill level of players is wide between the two teams.

Pretty much on the spot, though focused dps (especially late game) will actually work quite fine. Bramble is good anytime, but it's most effect early game. Mid to late game, it's popped fairly fast by UB, Reg, ect. It's still amazingly useful, just that QoT herself can be killed rather easily.

A good QoT will know this though, and either bait you or have an escape plan. People complain about the shield, but given time they'll get used it to and then....you know, work as a time to combat the issue. Which doesn't happen as often as it should.

Shield usually isn't a problem for me, I play torchbearer mainly, fireball, deep freeze, rain of ice, and fire nova are all enough to take down a shield. I played a game with a tank rook and a QoT with an oak as my partner and we absolutely shredded her and the rook.

If it's 1v1 with a QoT and they put up the shield, the only intelligent solution is to go away. it doesn't last forever. Just leave, or you will regret it. In a 2v1 situation, depending on classes, you may be able to plow through her shield. As an exclusive QoT player I'd say the only people who are a real threat to my shield are the unclean beast and torch bearer. Fireball will either take it out or remove most of it, unclean beast's spit eventually gets through it, it at least makes me have to retreat if i'm out of mana and/or have no healers around me.

I wouldn't waste any kind of stun or disrupt on a bramble shield cast though. That seems unwise. The purpose of those abilities are to stop escape so you can get the kill.