As a surviving spouse, can I rent the property to someone?

If the property was owned by you and your husband as "joint tenants with right of survivorship" or "JTROS," which is a common way for spouses to own, the house became yours automatically on your husband's death, does not become part of his estate, and is not inherited by anyone else.
If the property was titled solely in your name, it remains yours.
In either situation above, you may do whatever you want with the property and are its sole owner.
If you and your husband owned the home as "tenants in common," then you still own your 1/2 share of the property and get 1/2 of your husband's 1/2 share (so are a 3/4 owner), while the 19 year old gets the other 1/2 of your husband's share, and is a 1/4 owner.
If the house was titled solely in your husband's name, then you and the 19-year-old each inherit 1/2 the house.
(When there is no will, by the way, who inherits what is set out by the rules for "intestate succession," which vary somewhat state-by-state. The above is for Mississippi.)
If you and the 19 year old are both owners, you both have the right to use, occupy, profit from, etc. the house. To avoid later legal fights (since you both would have rights to the house, you could either of you try to enforce those rights in court, if the other is doing something you don't like or agree with), as a practical matter, you need to either work things out with your co-owner (such as entering into an agreement to lease out, or sell, or othewise use, the home), or else should sell the home, split the proceeds in the appropriate shares, and go your separate ways. If one of your wants to sell but the other does not, the one who wants to sell can bring a legal action traditionally called an action "for partition" (your state may have a different name for it) and get a court order requiring the sale of the house.
A good idea would be to consult with a real estate attorney and let him/her help you with this situation.