Nostalrius Begins - Quality wow vanilla realm (1.12)

Im level 39, with 40 gold.
What is the best way to farm gold for the mount?
I have skinning and LW as professions.

Try to save up your gold, if you have limited spending you should have enough by like level 44-46.

Additionally you can farm Fire and Earth Elementals, although don't be surprised if a level 60 is doing the same thing.

Having recently just stepped aside from questing to do this I can tell you what I did. Took me only 2 days @2-3 hours of farming because I work full time so its all I had time for out of a day. Go to Badlands and farm lesser rock elementals for elemental earth. The elementals here drop pretty good vendor trash, solid stones and deeprock salt which can be sold on AH for decent coin.

I don't know if the quest is implemented, but in the coastal village in Desolace (I forget the name) there is a troll on the dock who accepts stacks of something (fish, crabs?) from the crab cages in the water off the coast for $. If you can find someone to craft you the +swim speed belt (from Tailoring), I believe it's pretty decent money and the Makruras that are sometimes spawned by "failed" cages aren't terribly difficult to kill. YMMV, easier for classes with water-breathing capabilities.

I agree with farming rock elementals in Badlands, gives money+exp at the same time

Don't train your skills for your new levels. Or if you do, only train the skills you will use often. This will help save lots of gold.