Once upon a time I read an old magazine that had reminisces from old timers. One old person wrote that when he was a child he and his brother, both young children, were sent to drive a wagon on a long trip to town for some business. They met a cavalry patrol and were told a war party of hostile Indians was in the area.
I also remember reading something where General Sheridan, in command on the plains, complained about the careless way the western settlers would let their women and children make dangerous trips unprotected.
Around 1855, Isaac Stevens, territorial governor of Washington, sent his thirteen year old son Hazard Stevens (1842-1918) on a long ride with an important message, a ride compared to the famous ride of "Portugee" Philips in 1866.
You may have heard about Madeline de Vercheres (1678-1747) left in command of her parents settlement and fort at the age of 14. https://en.wikipedia.org/wiki/Madeleine_de_Verch%C3%A8res
You may remember that in the age of sail it was common for British naval officers to begin their careers as apprentice officers at the age of 12 to 14, and had some degree of authority. Sir John Theophilius Lee began his naval career at the age of nine, and was ten years old at the Battle of the Nile in 1798. After the battle he as sent with a ship's boat to try to retrieve floating masts and spars and thus had his first command at the age of 10.
In the US Navy Admiral David Farragut (1801-1870) became a midshipman at the age of 9 and had his first command at the age of 12 when in command of sailing a captured British merchant ship to port, and was later wounded and captured at the age of 13.
According to Cassius Dio Roman history LXXII
Marcus Antonius remained in Pannonia in order to give audience to the embassies of the barbarians; for many came to him at this time also. Some of them under the leadership of Battarius, a boy twelve years old, promised an alliance; these received a gift of money and succeeded in restraining Tarbus, a neighboring chieftain, who had come into Dacia and demanding money and threatening to make war if he should fail to get it.
So if Merry was the equivalent of a human 12-year-old, so what? There are plenty of examples of human 12-year-old children being entrusted with much more important duties than watching the house while Frodo took a nap.
PS - I have heard of a practice called babysitting, in which teenagers or even younger children are hired to watch, and if necessary, protect younger children.
PPS - I remember when I was a child walking to elementary school the intersections near the school had crossing guards to help the children cross the streets safely, and those crossing guards were older elementary school children.
So those are more or less contemporary examples of children being given more important tasks than watching Bag End while Frodo took a nap.
PPPS - Of Frodo's four upper class friends mentioned in "The Shadow of the Past"
Folco boffin was born in SR (Shire Reckoning) 1378, Fredegar Bolgar was born in SR 1380, Meriadoc Brandybuck was born in SR 1382, and Peregrin Took was born in SR 1390, and Frodo's gardener Samwise Gamgee was born in SR 1380. The Farewell Party was in SR 1401.
So Merry was the youngest of Frodo's friends except for Pippin, and was probably chosen to watch the house because he happened to be around when Frodo wanted to take a nap.