Legally, yes you can buy. Practically, most 19 year olds don't have the funds for down payment, the job security or credit history to obtain a loan. My question for you, "are you most 19 year olds?"
Because you want to own a house, whether now or in the near future, here are a few things you can do to make that more likely when you decide to.
Mind your credit. Don't get caught up in the ease of "low monthly payments" and buy everything under the sun. Sales people will push their cards along with the merchandise at everything from hardware stores, to electronics and clothing stores. Having some credit is necessary to demonstrate you are responsible. Having too much will hurt you. Abusing it by running up high balances, paying late and or skipping payments will kill your dream of home ownership for a while.
If you are not going to be a full time student soon, then get a job you love and stay put. Job hopping is tough on credit and the security that lenders are looking for. Especially if you change the type of work you do. If home ownership is your goal, then you need to not chase other goals which don't mesh with that one.
Now, please understand, I'm not advising you to for go your youth, education and experiences to become a mortgage holder, that is entirely up to you. If home ownership is your goal just be prepared to say no to other things.