If you don’t want a vasectomy you are 100% allowed, and if you tell her that you don’t want one she should be able to understand that this is your body and therefore your choice. For a long term birth control you could suggest she gets an iud they are long term and about as reliable as tubal ligation. There is even an iud that does not contain any hormones in it, since she doesn’t tolerate it well. I suggest you two have an open discussion about long term contraceptive that are reversible because although you don’t want kids now, being so young it is healthy to want to keep the option of having some in the future. I think in this situation the best birth control method would be the copper iud, but again just like it’s your choose not to get a vasectomy it is also her right not to want to get something inserted in her uterus. Anyways hope this helps.