Advice on mortise& tenon?

A good "rule of thumb" for mortise and tenon work is 1/3 the thickness of the stock, or the next larger common size. For 1" thick material I would go with 1/2" mortise and Tenons.

Look into making the mortises using a guide bushing on a plunge router, the correct size spiral bit, and a template with it's hole the width of the chosen guide bushing and the length determined by how long you want the mortise, plus the difference between the bit and the outside of the bushing for each end of the mortise. Make your template out of thin plywood, tempered hard board (MDF), plastic, etc. Attach some guides so it's easy to position and clamp it to your work. Set the depth of cut for the router. Make many overlapping plunge cuts into the work being guided by the bushing and template. When the bulk of the wood has been removed, slide the router back and forth to the ends of the template to clear the remaining wood, and the mortise is complete.

If you make a mortise in both joining pieces, it's easy to make tenon stock the needed thickness using a table saw or surface planer, then cut a piece the size you need to fit between these two mortises. This is called a "Floating Tenon" but it doesn't truly float, because both ends get glued into the mortises. The quality of fit of the sides of the tenon to the sides of the mortise is important. It needs to rub, but not require a hammer. You need room for the glue, but the pieces should not fall apart when dry fit together without glue. It's much easier to size a tenon to fit a router mortise than size a mortise to fit a tenon. The mortise gets cut with a standard size router bit. Size the tenon to fit the mortise that it makes. Chisels and mallets should not be required.

Charley

Tom did mention round holes with a router, I guess he means something in the Domino style.
I agree that 1/4'' tenon is way too small. We do not know the load factor for this bed ! how much weight will be on it. How much activity(LOL) would also be a factor. If the combined weight is 200 lbs or 400 lbs it makes a substantial difference. If you are 30 years old or 70 years old will probably make a difference. If you have 2 or 3 young children that like to jump on your bed on a Saturday morning to wake you up will make a difference.
To be on the safe side, I would use 8/4(2'')hardwood rails that are at least 6 to 8'' wide with 1'' mortise and tenons. I also think that the mechanical hardware is a good idea. If a headboard is in the picture, bolting it to the wall securely will also help. Another possibility is to use a combination mattress and box spring with a metal frame and then the wood rails can be purely decorative. Seeing a question like this makes me appreciate my mortising machine !