I think it is nice to consider adopting a pet. Just make sure you know that having a pet is a lifetime commitment. People wouldn't give up their children, but they do their pets, hence 5,000,000 killed annually in the US each and every year. Having a pet is not for "as long as the pet conveniently fits into your life, but a commitment for as long as the pet lives.
So, some things to consider:
Do you travel, vacations, camping, etc? Who will care for your pet?
Is having a pet too much for you right now with two toddlers? They certainly won't be able to help you at all with the care. Will you be able to handle the extra chores or do you want to wait? (Cleaning up poop daily, potty training if necessary, training at socializing pet all take time.) You absolutely cannot leave your dog outside while the family is inside.
Who will walk, train and groom the pet? Will you take your dog to the groomer? That costs money too. An active pet may require weekly baths.
Make sure you do your budget and include food, supplies (bed, leashes, collars, tags, license each year, pet shampoo, food, snacks, toys, etc).
Make sure to budget your vet care. At first, its an annual and vaccines but as they age, dentals alone can cost a few hundred. Don't forget to consider vet care as the pet advances in age. It can cost hundreds per month. What if the pet gets cancer or needs a surgery for a cyst, lump, bad tooth, etc? Are you financially prepared?
This was not meant as a lecture but many people get a pet and don't consider all of the time and money it takes and the pet ends up BACK in the shelter. Shelters are overflowing with unwanted pets, because of a simple lack of commitment.
Also, make sure the pet is introduced to your children at the shelter. Will you need gates in your home to keep your youngest from playing with the dogs food? Will you be getting your dog a companion too? What happens as the children get older and are spending more time with their friends, at school and activities? Have you considered that? They are 2 and 4 right now and giving in to their wishes or preoccupations when an actual LIFE hangs in the balance is a serious matter. Get them one of the toy hamsters or something if you have questions, doubts or any concerns.
I think both your kids are old enough to go to the shelter but it may be overwhelming, a little. Explaining to your kids they will have this pet until they are out of high school won't mean much to them necessarily right now but telling them that is why you are not getting a pet will, if that is your best decision.
Getting a pet is a lifetime commitment.