Golf me an HQ9+ Compiler

Actually, 17 bytes

"HQ9"∩εj'N'9(t'.j

Try it online!

This program compiles HQ9+ to Actually.

Actually is (almost) a superset of HQ9+ - the only difference is that the 9 command in HQ9+ is N in Actually. Because + is a NOP in HQ9+ (the accumulator is never actually used or displayed, and thus many implementations treat it as a NOP), it is stripped out.

Explanation:

"HQ9"∩εj'N'9(t'.j
"HQ9"∩εj           strip all characters not in "HQ9", preserving order
        'N'9(t     replace all occurrences of "9" with "N"
              '.j  insert a "." between every pair of characters

-1 byte from Christian Irwin

Java only 551 bytes

Joined in on the fun! This is a java compiler which compilers HQ9+ to java.Java is not verbose at all. Some code shamelssly stolen borrowed from "99 Bottles of Beer".

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public class a{public static void main(String[]a){System.out.printf("public class a{public static void main(String[]z){String p=\"%s\";for(char a:p.toCharArray()){if(a=='H')p(\"Hello, World\\n\");if(a=='Q')p(p);if(a=='9'){String b=\" of beer\",c=\" on the wall\",n=\".\\n\",s;for(int i=100;i-->1;){s=\" bottle\"+(i>1?\"s\":\"\");p(i+s+b+c+\", \"+i+s+b+n+(i<2?\"Go to the store and buy some more, 99\":\"Take one down and pass it around, \"+(i-1))+\" bottle\"+(i!=2?\"s\":\"\")+b+c+n);}}}}public static void p(String s){System.out.print(s);}}",a[0]);}}

Mathematica, 453 bytes

"("<>#~StringReplace~{"H"->"Print[\"Hello, world!\"]; ","Q"->"Print[ToString[#0, InputForm]]; ","9"->"a = StringJoin[ToString[#1], {\" bottle\", If[#1 < 2, \"\", \"s\"], \" of beer\"}] & ; b = StringJoin[a[#1], \" on the wall\"] & ; Do[Print[b[i], \", \", a[i], c = \".\n\", If[i < 2, StringJoin[\"Go to the store and buy some more, \", b[99], \".\"], StringJoin[\"Take one down and pass it around, \", b[i - 1], c]]], {i, 99, 1, -1}]; ",_->""}<>") & "&

"99 Bottles" code adapted from @alephalpha's program. Outputs a function that, when run, will print the output. (Could probably still find a less verbose quine method.)