Keep the transmitting and receiving antennas a few wavelengths apart to prevent damage, farther if you're using an amplifier. You can transmit right next to the RTL-SDR with an HT if you disconnect the antenna from the SDR. It will still receive the signal from across the room.
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Can you define few? Because with 2m wavelength it can make a big difference lol. Like 3 wavelengths?
I wouldn't go any closer than 2 wavelengths. 3 or more would be preferable.
10 dBm is 0.01 Watts or 10 mW, so you're right about being cautious. That said, short of physically connecting your handheld to the RTL-SDR, for short transmissions you're unlikely to break anything. A much easier thing to break is inadvertently turning on Bias-T and doing damage.
That's not to say that your handheld won't overload the dongle, it likely will, but that's also true for the AM and FM transmitters nearby. To do any amateur work with the dongle, look into broadcast filters.
Look at rtl_power as a way to discover strong signals across the bands. Your dongle as-is will give you years of fun and exploration.
If you want to check out the emissions from your handheld, look into getting some attenuators.
As a point of reference, I'm using a 10 dBm beacon that has been heard on the other side of the planet.
Source: Welcome to the hobby, 73 de Onno VK6FLAB