Possible broken transmission/motor mount in 2007 Toyota Yaris?

I bought a 2007 Toyota Yaris about 12,000 miles ago in March of this year. Automatic transmission, it now has around 72,500 miles on it. Recently, I have noticed a “clunking” sound/feeling when I shift from park to drive while on an incline. It doesn’t matter if I am going from park to reverse, or visa versa. It is more of a feeling… like something is broken and shifting forward or backwards more quickly/violently that it should, but I can hear it slightly. There is no such sound/sensation on level ground. Temperature/weather is not a factor. Is this a symptom of a bad motor mount/tranny mount? I had a bad motor mount on a previous car, and experienced a rattling noise while idling. There is no such noise or vibration with this car. I do not have a stable mechanic yet and would like an opinion before I try and establish a relationship with one (considering I am a small 25 year old woman who looks 17-18 years old, and I am not normally taken seriously). Any input would be appreciated. Thank you.

While it is possible that you have a bad mount, I tend to doubt it.
Instead, I think that you are hearing and feeling the release of the “park pawl” inside the transmission. This can result from some previous damage to the pawl, or it can result from not applying the parking brake/e-brake firmly enough, or from a parking brake/e-brake that needs to be adjusted. If there is too much pressure on the park pawl when it is released, it can make this type of noise on many cars.

Here is my suggestion:
The next time that you park on an incline, before you put the shift lever into the “park” position, apply the parking brake/e-brake very firmly while simultaneously holding down the brake pedal. Then, place the shift lever in the “park” position. Then, release the brake pedal.

When returning to the car, after starting the engine, hold the brake pedal down, shift from “park” to drive or reverse, then release the parking brake/e-brake. If the clunking sound/feeling is diminished or absent, then you know that you just need to modify your technique in the future. If it doesn’t make any difference, you might try having the parking brake/e-brake adjusted when the car is next serviced.

What VDC said. His technique is exactly what I’ve been doing for years when I have to park on any kind of incline. All cars will do what your Yaris is doing to some degree or another. There’s a lot of pressure on the parking pawl when you’re parked on a hill and the transmission lock is the only thing holding the car. It’s best to use the parking brake—after all, that’s what it’s for.