Linking verb, "is". It joins 'to do' with 'to get'.
 All I want to do is to get some sleep. or
'to get' is a restatment of 'to do'. The second 'to' is redundant, so speakers often leave it out,
 All I want to do is get some sleep.
or they leave out 'to do',
 All I want is to get some sleep.
'to' of 'want to do' is part of 'want', not 'do', which is why  is not an option:
 *All I want do is get some sleep. (ungrammatical)
All the best,