As you suspected, brass hose fittings are known to contain lead, which can cause severe health problems of many types. It doesn't take a lot of lead to be dangerous, and some studies even find lead poisoning in children who drink out of hoses while playing in the yard.
Several sources say not to drink from a hose with brass fixtures, even if the hose itself is rated as safe.
I'd be especially concerned in your proposed set-up, because even if you shut it off, residual water can sit in the top horizontal section of the fixture. That water has more time to be affected by the lead in that section, before making its way down through the other lead-containing brass fittings.
A number of studies emphasized that even hoses marketed as safe to drink from only include the hose. The brass fittings are studied separately, something many people don't realize.
From Consumer Reports:
Is it safe to slurp from a garden hose? I recommend that you don’t... The brass fitting on the ends of the hose are also likely to contain lead. Based on some testing we did a few years ago, water left standing in the hose can absorb worrisome amounts of lead and turn your first gulp into a health hazard.
From The Cleveland Clinic in Ohio, United States:
Dr. Allan said some hoses are made without harmful chemicals, and are marked as such. He said the hose fixture matters as well. Brass fixtures, for example, release lead which will contribute to health risks.
From Is your garden hose safe for drinking?
Mind the Fixture:
Most of the outdoor fixtures are made of brass. The brass is unregulated, and most of the time it contains lead... be always mindful of the fixture and if you have the money, change it regularly.
Backyard Boss also says that toxins can be present in the fittings, and the only way to be really safe is to just skip drinking from the hose.
In conclusion, it really isn’t a good idea to drink from a garden hose... it may also pick up extra toxins or pollutants through your garden hose or fixtures and fittings.
The State of California in the United States has very strict regulations regarding the safety of drinking water, listed in the California Safe Drinking Water and Toxic Enforcement Act of 1986. Brass hose fittings are not regulated, even though they've been found to contain significantly unsafe levels of lead in many studies.
Unlike residential plumbing fixtures, which must comply with the Safe Drinking Water Act, the brass fittings on hoses are not regulated, even though 30 percent of those tested in the study were found to exceed safety limits for lead. Source
In California itself, however, brass hose fittings have to be marked with a warning. See here for a hose nozzle with the warning attached.
California Proposal 65:
The brass in this product contains lead, a chemical known to the State of California to cause cancer or birth defects or reproductive harm. Wash hands after handling.
I strongly suggest seeking a safer product. Now that you're armed with respected information, you won't fall prey to someone trying to tell you it really doesn't matter. Check local or online garden supply companies. Find safe-minded gardening organizations, many of which are parent groups, and ask what they're using. Building supply stores can work too, just be firm and tell them not to sell you a brass product.