This seems fun.

Since you say news has just arrived that Beijing has fallen to the Manchus, I take it you mean in 1644. The good news here is that, depending on where you are, you should have reasonable chances of making it. The key to the Manchu takeover of China was, after all, winning over Ming officials and granting them Qing titles and positions. The main brunt of the Qing offensive south of Beijing was after all commanded by Han Chinese renegade generals like Geng Zhongming and famously Wu Sanggui, who had just defected. The Qing were highly interested in painting themselves as a legitimate Chinese dynasty and absorb as much of the Ming administrative apparatus as they could. Generally defectors were welcomed and would be allowed to keep their positions and salaries, provdied they swore fealty to the Qing Emperor. They also had to shave their head and have a Manchu queue, as the hairstyle was considered the ultimate proof of submission.

If you have moral qualms over betraying the Ming dynasty, you would have to join one of the rebel factions. Immediately after the fall of Beijing a court was established in Nanjing under a Ming pretender, the Longwu Emperor. He sought to maintain a large part of the Ming infrastructure, and he was the natural rallying point for Ming loyalists in the first years. If you feel loyal and don't want a haircut, you will likely swear loyalty to him.

The Longwu Emperor lost his position fairly quickly, dying by 1646. After this, Ming loyalty eventually consolidated to two power bases. The Yongli Emperor, a final pretender, established himself in a power base in the Yunnan province in the Southwest of China, rather far from Beijjing or Nanjing. You could evacuate along with him here, and hope for an administrative position here.

The other option is to join the leadership of Zheng Chenggong, otherwise known as Koxinga, the Ming loyalist pirate leader, who establishes his powerbase in Xiamen on the southeastern coast. he nominally swears loyalty to the Yongli Emperor, but is de facto independent. By 1662, Zheng will evacuate the Chinese mainland entirely and move his base to Taiwan, you can follow. Be wary that he has a short temper and a tendency to execute his subordinates when they displease him.

If you are highly unlucky, you may end up in one of the regions that comes under the rule of peasant revolt leaders like the Yellow Tiger, Zhang Xianzhong. He was welcoming to officials at first, but as pressure clamped down on him, he accused them of treason and massacred them.

The lucky part is, that as long as the war went on, the Qing kept welcoming defectors with a pardon and a new title and position, as long as they swore loyalty and attained the Manchu hairstyle. This kept on until all resistance was quelled.

All things considered, I don't think the options are that bad. There was generally an escape path.

For my source material at this, please check:

On the Trail of the Yellow Tiger: War, Trauma, and Social Dislocation in Southwest China during the Ming-Qing Transition by Kenneth Swope and

The Lost Colony: The Untold Story of China's first Great Victory over hte West by Tonio Andrade