I'm going to discourage my girlfriend from following her dream career
Why don't you want her following her dreams?
I'm not sure if I can handle the hard work and the financial burden
It's mean to not be supportive of your gf's dreams. You should be encouraging towards her.
It's cool with me as long as she doesn't go chasing her dreams.
Well I think you should be supportive of whatever she wants to do in life. Otherwise she may start to resent you.