。
I'll plunge straight into the work.
Literal
Vigorously work [to-に] set-about.
どしどし is a reduplicated mimetic/adverbial meaning 'energetically / vigorously / without hesitation' — often used to encourage someone to do something freely and plentifully (どしどし応募してください 'please apply freely'). 取りかかる is the compound verb 取る + かかる (literally 'take and hang on') = 'to set about / begin work on,' with に marking the object of the activity.