There are a variety of sites and locations to purchase a pet stroller. The one we purchased is this model -
It works well for our 15 pound cat and he very much enjoys going for rides. As he is enclosed, he really doesn't even care about passing dogs either.
He even likes to sleep in it when we aren't going any where (so it would make a great emergency kennel or place to put your pet when company comes over. We paid $90 for ours and have had it for about 5 years and the only wear that is visible is on the top screen (because our cow of a cat likes to sleep on there too). Prices range from quite reasonable to OMG! (There is even a model designed by JEEP®, insert eye roll here).
So, rather than carry your little dog in your purse or wonder forever what happened to kitty; I recommend a pet stroller highly. Yeah, some people will snicker; but ask them what happened to their cat and they'll have a tragic tale for you. Pet strollers are also great for suburban or city dwellers who don't have the luxury of a field to let their furry friends romp through.
For you antisocial souls out there (raises hand). this also keeps strangers from messing with your pet. You don't want me ruffling your kid's hair, do ya? So keep your mitts off my pet.
Pet stroller. Get one. Your furry children will thank you.