Your first car! You must be excited
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I have two Yorkies. We (meaning my husband and I) don't go out that often, so usually only one of the dogs is out at a time. However, this one is plenty large enough (I ordered the medium) to handle both dogs (I ordered an extra safety strap so they each have their own), or allows plenty of "lounging" space for one dog.
The drawer on the bottom is very nice to hold their stuff. It's not as fancy as the Stow and Go, but for us it's more practical. I have a Jeep Grand Cherokee; it will fit in the passenger front seat or takes up one passenger seat in the back (leaving room for one or two other passengers). It's high enough for them to look out and enjoy the passing scenery.
Lookout II Pet Safety Car Seat at Precious Pets Paradise There are other sources, too: Google "lookout II" + Snoozer for more information and cost options.
I purchased the grey "pleather" to match my car's seats; the cover comes off and is machine washable (but because of the pleather, needs to be line-dried. The other styles can go in the dryer, too).
If you travel a lot and do overnighters, the Stow and Go would probably be a better option for you. But if you just do "trips", then the Lookout II would probably be a better fit for you and your doggie, while leaving enough $$ left over to buy some new toys or a dress or something