I don't think being on benefits makes you undeserving.
Which benefits do you receive? I'm guessing ESA and DLA/PIP?
If you're on ESA I had a quick look, and it seems like you can go abroad for a maximum of 4 weeks on holiday without it affecting your benefit but you'll need to tell the jobcentre.
Employment and Support Allowance (ESA)
There are 2 types of ESA - income-related or contribution-based.
You can get both of these for 4 weeks if you go abroad.
Talk to your local Jobcentre Plus before you go.
Going abroad for more than 4 weeks but less than a year
Tell your local Jobcentre Plus if you’re going abroad for more than 4 weeks.
You can carry on getting contribution-based ESA for up to 26 weeks if you’re going abroad for medical treatment for yourself or your child.
It doesn’t matter which country you go to.
I personally would question if it's the right time for you to. If you live in supported housing then it would suggest you need daily help with living due to your illnesses. Travelling abroad, especially somewhere so far away, is quite demanding and if you were alone how might you cope if there was an emergency like having your passport stolen, or getting lost somewhere remote?
Could you do a test run first somewhere in the UK to see if you can manage by yourself for a week or so?