It's important to remember the timing; even intrasystem subspace jumps aren't instantaneous. Simms states that a jump from Mars to Jupiter is roughly 5 minutes. So, assuming you do send a courrier, the message won't even be received until several minutes after the courier has departed. By the time reinforcements/assets arrive, you're looking at roughly 10 minutes (maybe longer) before any kind of help arrives. And when that help does arrive, their knowledge of the situation as at least 10 minutes out of date, and if they can't jump out of there quickly, they could become victims themselves.
And really, she didn't even need it. If she wasn't just serving as high-level bait for a grand trap/gambit, she could have won (or averted defeat, at least) by holding all of her forces in reserve until the full UEF strikeforce jumps in, and then sortie most of the air wing to flash/shock-jump and gank the Hanuman (which the Deimos corvettes could help with significantly themselves, with their slash beams/overdriven slash beams). With that done, the entire battlegroup unleashes its overdriven beams (including the Carthage's!), focus-firing on one ship at a time, while the air wings engage the Uriel gunships from both in front and behind, with their own capships providing fire support/protection as well.
As for how to truly defeat/nullify the Uriels? Those Aeolus cruisers--uber flak spam. Deimos corvettes add in their own AAAf's/flaks, and the fun begins.
It would still be--at best--a close fight, but it would make the battle attritive, not decisive, and losing most of the Wargod strike force would be an unacceptable price to pay for anything short of killing the Carthage...and BFGreens are nothing to sneeze at, especially when supplamented with SGreens, TerSlash's, ungodly amounts of flak fire, and lots of torpedo and Maxim strikes. And for every ship the Wargods lose before really going in for the kill on the Carthage is a significant chunk of firepower lost--meaning that taking down the Carthage will be a longer, costlier, and more difficult task.
That said, the Carthage and her battlegroup definitely had time to send a detailed report/distress call when the group jumped to Saturn (before the Indus, let alone the Hanuman, showed up). And if a single Chimera was unaccounted for, or could be spared from the other engagements, then things would get really ugly, really fast.