The irony of trust
This speech seems to presume trust, but is Queen Elizabeth really trusting? She starts by commenting about rumors of dissension in her ranks, so the speech is not only about trust; it is also specifically designed to engender trust. Although she wants to believe the best about her troops, she is clearly attempting to rally them, so she must believe they need rallying. Ironically, the trusting speech seems predicated on confusion and mistrust.
The irony of warfare
Here's a grand irony about European history: They invoke God's blessing on warfare very often, which is very normal human behavior of course. There is clearly an honor to be gained in the battlefield (this has been the consensus in every world mythology ever invented except a few). The irony is that they are fighting for the Christian God who explicitly forbids warfare. It is ironic to celebrate war whatsoever, especially in the name of a Jesus who clearly preached non-violence.
The irony of gender
Queen Elizabeth comes right out and addresses a major source of dissension in her ranks. She governs an army that has their doubts about a woman's intuition in warfare. She boldly claims that she has as much insight and courage as any king could have. She assures them there is a natural irony in their perception of gender, and that they can trust her. Without trusting her, she feels they will falter.
The irony of risk and reward
She reminds her army of the rewards of victory. She promises not only spoils for the troops who fight, but also actual reward in the form of payment. This is ironic, because it underscores what the army is really feeling: terror and the true dread of death. Is the risk worth the reward? Perhaps it might be! The queen feels the reward would be enough to permanently improve the lives of the veterans who serve her.
The irony of community and warfare
These troops are not like professional combat-trained troops as in today's militaries. They are actually just community members in need of safety. However, the governments of Europe have chosen warfare for these folks, so this speech is not like a speech to trained professionals, it is a speech to fathers and brothers. The irony is that the actual communities are having to fight together for survival, against another community from somewhere else. The irony of fighting to preserve peace is clearly evident.