The spelling of the word "doest washing" is not commonly used in modern English. However, it can be seen in older texts as a variation of "does washing". The IPA transcription of "doest" is /ˈdʌst/ which is pronounced as "duhst". This word is the second person singular present tense of the verb "do" in Early Modern English. Similarly, the IPA transcription of "washing" is /ˈwɒʃɪŋ/ and it is pronounced as "wosh-ing". The word refers to the act of cleaning with water and soap.
The phrase "doest washing" does not have a clear etymology as it is a combination of two words: "doest" is the archaic form of the second person singular present tense of the verb "do", and "washing" is the present participle of the verb "wash".
The word "do" originated from Old English "don", which can be traced back to Proto-Germanic "dōną". It has been used in English since the early medieval period and has evolved over time.
"Washing", on the other hand, can be traced back to the Old English word "wascan", which derived from Proto-Germanic "waskanan". This term has remained relatively consistent in its meaning throughout history.
Therefore, "doest washing" would refer to someone who is presently performing the act of washing as expressed in archaic language.