Is it permissible for a woman to wear short clothes when she is on her own?

Firstly: 

We praise Allah, may He be exalted, for having guided you to Islam and enabling you to follow the path of adherence to its sublime rulings and teachings. We ask Allah, may He be exalted, to make us and you steadfast in following His religion. 

Secondly: 

There is nothing wrong with a woman wearing whatever she wants in her house, of clothes that women customarily wear in their houses, so long as she is certain that she will not be seen by men, as you say, and that they will not suddenly come into the place where she is. 

But, if a woman is face-to-face with a non-mahram man, inside her house or outside, then she is obliged to observe hijab by wearing the clothing that is prescribed in Islam: the abayah and head cover that covers all of her body and adornments. 

Allah, may He be exalted, says (interpretation of the meaning):

“And when you ask (the Prophet’s wives) for anything you want, ask them from behind a screen, that is purer for your hearts and for their hearts”

[al-Ahzaab 33:53]. 

“O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies (i.e.screen themselves completely except the eyes or one eye to see the way). That will be better, that they should be known (as free respectable women) so as not to be annoyed. And Allah is Ever OftForgiving, Most Merciful”

[al-Ahzaab 33:59]. 

See: Hiraasat al-Fadeelah by Shaykh Bakr Abu Zayd, p. 25 

With regard to the limits on what a woman can wear in her house in front of her children and mahrams, or in front of other women, please see the answers to questions no. 34745 and 6569.

And Allah knows best.