Digit Date Range

R, 81 bytes

function(s,e,n,x=seq(s,e,1))x[lengths(sapply(strsplit(paste(x),""),unique))==n+1]

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Uses R’s native date format and has leading zeros on day and month.

Red, 93 bytes

func[a b n][until[if n = length? exclude d: rejoin[a/4"-"a/3"-"a/2]"-"[print d]b < a: a + 1]]

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Without leading 0s for days/months.

Too bad that Red converts internally 09-10-2019 to 9-Oct-2019 - that's why I need to extract the day/month/year individually.

Japt, 23 bytes

Takes the date inputs as Unix timestamps, outputs an array of strings with formatting and leading 0s dependent on your locale. Would be 1 byte shorter in Japt v2 but there seems to be a bug when converting Date objects to strings.

òV864e5@ÐX s7Ãf_¬â ʶWÄ

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òV864e5@ÐX s7Ãf_¬â ʶWÄ     :Implicit input of integers U=s,V=e & W=n
òV                          :Range [U,V]
  864e5                     :  With step 86,400,000 (24*60*60*1000)
       @                    :Map each X
        ÐX                  :  Convert to Date object
           s7               :  Convert to locale date string
             Ã              :End map
              f             :Filter
               _            :By passing each through the following function
                ¬           :  Split
                 â          :  Deduplicate
                   Ê        :  Length
                    ¶       :  Is equal to
                     WÄ     :  W+1, to account for the inclusion of the delimiting "/" or "-"