Yes, the OID is encoded in the binary data. The OID 1.3.6.1.5.5.7.48.1 you mention becomes 2b 06 01 05 05 07 30 01 (the first two numbers are encoded in a single byte, all remaining numbers are encoded in a single bytes as well because they’re all smaller than 128).
A nice description of OID encoding is found here.
But the best way to analyze your ASN.1 data is to paste in into an online decoder, e.g. http://lapo.it/asn1js/.