No way to tell really. It depends on the size of your brooder, whether it's totally contained (glass or plastic vs. wire), how close the lamp is to the brooder, where the brooder is being kept, etc. Your best bet is to lay a thermometer on the floor of the brooder under the lamp and see what the temp is. I know nothing about quail, but for chickens I'd want 95-100 directly under the light for the first several days...
If a 250 is too much, you can always move it further from the brooder...or try a 150.
I have an entire array of regular light bulbs for brooding. I hatch both quail and chicken chicks. I have a brooder house for the chicken chicks that they go to after 10 days. My quail babies may end up there this hatch as it is colder than expected this year.
So start with a 125 watt and see what the temp is in your set up. (Brooder light and thermometer should be dedicated just for that brooder setup) If it doesn't get to 95 degree, use a larger wattage. Make the set up so you can raise and lower the light easily. I usually end up raising the light during the day and lowering it at night. About every 5-7 days, I am changing to a lower wattage. So I keep 100,75,60,40,25 wattage just for my brooders. (Brooder house uses 40-25 in winter-summer for the last little bit)
I brood my chicks in the house in rubbermaid tubs for their first 10 days then out they go. I start with 100 watt. But out in a shed you will probably need a higher wattage. You may need the 250 watt, I use one in the winter (February sometimes) for my Brooder House. You just have to try it and see, at different times of the year you will use different wattages. You should also have extra's in case the thing burns out on you when the stores are closed or 10 O'clock at night when you don't want to run to the store, so get 2 of each. Seems to happen all the time.
Brooder temperature is something you end up playing with at each hatch. Gives you an excuse to check on the babies and admire them while they are still cute. And plan out recipes according to their size.
Remember 95 1st week, 90 second, 85 third, 80 degrees until completely feathered during that 4th week.
250W bulb is an overkill for most indoor operations, unless your room is at 40-50 degrees or you brood hundreds of chicks.
I use 60-75 Watt bulb for smaller amount of chicks. For larger amount brooding in large wire cage I use dimmer switch to run 250W bulb that allows me to lower it output for the proper temp, amount of chicks and brooder size.
Also I never use thermometer for brooding since: this "100 degrees at hatch 95 second week etc. "mantra" is arbitrary and you can easy overheat chicks, I believe that most problems and early deaths come from over heatting.
IF YOU PLACE THERMOMETER on the brooders FLOOR USING INFRARED RADIANT HEAT (that's what 250w red bulb is) you will get FALSE reading since due to radiation thermometer will show higher temperature than ambient air!.
I let my chicks tell me their level of comfort and adjust the lamp accordingly lowering it or adjusting it's output by dimmer switch.
Keep in mind that 250W bulb going full blast is a fire hazard and a power hog.
At 15c per KHW rate it will use $25,00 worth of power in one month! If your rate is higher it will use much more. Do your math.
I have nothing against 250W bulb, I have 2 of them, also I have radiant heat white 150W bulb, but I use them all wisely and efficiently.