I'd call up a local glass and mirror shop and tell them what you are dealing with. They should be able to get you started or do the whole thing depending on what you are after.

Wow, what a bummer! Hope the dog is ok.

Is it leaded glass? If so I'd try asking at a lamp/lighting shop thinking they might know a local artisan who does leaded windows. Somebody at these related businesses should know how to fix it, right? :)

oh, yeah, the cost. My totally wild guess would be anywhere between $50 and $350+, depending on your location and how well your dog behaves. lol!

Is the glass broken or just popped out?

You might post this on the stained glass forum--there are some experts there.

It's not stained glass. It's wooden mullion. I think that's the word. Based on the way it broke, I'm almost positive that it's all small pieces of glass made to fit the segments, not one large piece with the wood on the top.
I think we have a glass store right around the corner. I'll have to give them a call.
The dog is fine. I haven't forgiven him yet. Haha.
Thanks!

The glass is held in by either glazing points and putty or thin wooden strips called glass bead. Putty will yield more readily to a bit of carefully applied heat that brute scraping force. A heat gun is very handy (be careful with any intact glass, because the heat will crack it in about 15 seconds.)
f you have wooden strips, they will have been secured with small brads, and need a lot of patience or you'll have splinters instead of glass bead. Pry from the center of the longest pieces with a putty knife to work it free.
To prevent rattling, seat the glass in glazing compound or clear caulk.
Casey

The glass shop should have everything you need. I would stay away from a heat gun, unless you use a shield to keep the heat on the broken section only. A putty knife--strange how the name fits--will remove the old putty if you are careful.
Take the old pieces with you, or measure the overall dimensions when you go--if you are lucky, they will cut the piece to the shape you need.
Secure the new piece with glazier's points, then putty the edges. A steady hand is all that is needed. Make sure the putty doesn't go past the edge of the muntin on the other side of the glass or it will be obviously repaired.
No need for an installer, just some patience and a few bucks for the glass and glazing compound and points.
I replaced the clear plain glass in my front parlor window with stained glass a few years back--it had wooden muntins except the shapes were all triangles and diamonds. A pain in the ass to do a 2.5'x5' window, but it looks nice when the sun shines through it.

If the excellent comments above haven't given you the confidence to proceed, try getting a copy of Working Windows at the library. It will talk you through whatever you need to do.

It's not as hard as you think--remember, human hands made that window originally. Of course, they were expert hands, but patience and trial-and-error can get you pretty far with these things.

I have no idea what Casey and Columbusguy1 are talking about so I think I will stick with a pro, haha. Someone from a glass store around the corner from me is going to check it out and give me an estimate.

Here is a link that might be useful: Absolute Glass

Katie,
I have no idea of the repair costs. You will need to talk to someone who works on leaded glass windows.

But, I do have a suggestion to prevent possible future problems - add a layer of plexi-glass - or even better "Lexan Polycarbonate" to the window's inside to prevent possible future breaks (hidden benefit less heat/cooling loss) if it is done well - visually and functionally.

I have been there and done that before with dogs.

Interior plexi-glass (or variations ) does help prevent recurrent problems - and ups the insulation value. I suggest Lexan because it is stronger than plexi-glass for most usages.

Leaded glass repairs are not cheap, protection of leaded glass can be done relatively inexpensively.

Some churches use Lexan as an outer layer to protect stained glass windows.

Dad