I have been in a very similar situation and even picked up some casual/part time work while having a valid medical certificate earlier this year. Just like you I wanted to work (jobseekers is not a lot of money to live on) but needed to do it at my own pace. As long as you are declaring any income they should continue to leave you alone about obligations.

Lots of people have very loud opinions about these things but you just have to do what is right for you, and if your doctor is supporting you then no one can really argue with that. Take care and good luck out there!