Lets assume the private key is 0000111122223333444455556666777788889999aaaabbbbccccddddeeeeffff
Both Bitcoin and Doge can share a common private key and use the same Elliptic Curve algorithms to synthesize public keys.
Here is a working example for how one can synthesize an uncompressed public key for Bitcoin or Doge from a common 256-bit hexadecimal encoded integer private key.
% echo "0000111122223333444455556666777788889999aaaabbbbccccddddeeeeffff" | bx ec-to-public -u
040d47568a5e517067a2836c3823fbc58169a7662bfae934a4d41da3e23c98d816e7202dd702ffe038147f78aee4973a581972960a1460312ffb6f3f0f13d4a52c
Here is how a compressed public key can be calculated for either Bitcoin or Doge. Notice the public key is half the size.
% echo "0000111122223333444455556666777788889999aaaabbbbccccddddeeeeffff" | bx ec-to-public
020d47568a5e517067a2836c3823fbc58169a7662bfae934a4d41da3e23c98d816
Computation of compressed and uncompressed Bitcoin and Doge addresses. One must examine this table to understand the version values [-v flags] that must be different for Bitcoin-based altcoins used such as Doge. Unsure if Doge fully supports compressed addresses, but is very likely to do so if the Doge source code forks are updated when Bitcoin is updated. Compressed addresses have been supported by Bitcoin for over 4 years.
% echo "0000111122223333444455556666777788889999aaaabbbbccccddddeeeeffff" | bx ec-to-public | bx ec-to-address -v 0
1PbStXjfDNBU6FZA2iSeisVWwCFN9GK1eQ (is a compressed address)
% echo "0000111122223333444455556666777788889999aaaabbbbccccddddeeeeffff" | bx ec-to-public | bx ec-to-address -v 30
DTjYRngJWn5kdFjkmJSDGdf7pKyfUnVnGg (is a compressed address)
% echo "0000111122223333444455556666777788889999aaaabbbbccccddddeeeeffff" | bx ec-to-public -u | bx ec-to-address -v 0
1NGoV1EGZrwM7yvUYqRC7TMBMj7ftpjR2B (is an uncompressed address)
% echo "0000111122223333444455556666777788889999aaaabbbbccccddddeeeeffff" | bx ec-to-public -u | bx ec-to-address -v 30
DSQu2GAusGqdez75HRQkfDWnErqyEB4Bov (is an uncompressed address)
Believe the answer is yes.