Dowels are probably your best bet for this fix because the tool cost is much lower for the case that you need to purchase tools to do this repair. The cost of a doweling jig is much lower than a biscuit cutter. Drilling the dowel holes is easily accomplished with an electric drill.
If you end up with just a one inch wide repair strip added in then I would just drill the dowel holes right through the strip and into the original material on each side. Do check your table top pieces for overall flatness after you separate the two sides from the split. Warped lumber often develops a curvature that spans a greater distance than just one inch. You'll need to take this into account when you decide to start trimming away the split edges.
With properly jointed surfaces on the two trimmed edges and the hardwood accent piece the dowels and glue should be plenty strong to hold things together.
You may want to cut the accent piece just a small bit longer than the amount needed and then trim and sand it to the existing round table edges after the gluing is done. This will give you the greatest opportunity blend the edge of the table to the nicest fit and look.
I see some challenge in clamping the round table to get good tight glue joints. You may need to fabricate some jigs to help provide a place to engage your clamps across the width of the table. The sketch below shows one idea of how to do this. Some flat boards about 4 -> 5 inches wide can have some blocks glued and screwed on the ends that will provide a place to engage the clamps.
I have shown the blocks somewhat offset from where they would actually be attached to the boards so that you can see the nature of how they would fit to the contour of the table edge. Long bar clamps or pipe clamps would be spanned across the table top at the overhang of these boards as shown in the next picture.
It might be good to consider a sliding dovetail.
Edit 11/16/13 To assemble your bed frame, the M&T joints with captured bolts with nuts to hold the corners together with the legs. Just as a mention, a good hardwood needs to be used for the assembly. regular 2X4, 2X6s and other similar materials used in the construction of homes will be too soft, and when the joints are put under stress SPF, Hem fir, etc is going to compress and loosen the joints. To use this material you need glue and screws to hold all this together. That is not an option for you I think?
To assemble this, white oak, ash, Black walnut and a dense variety of mahogany would be a good choice, if it is not cost prohibitive. There are other hardwoods too, just give a look. Red oak and Douglas Fir are hardwoods, but very prone to readily split under the stresses you are going to expose the joints to.
Another good thing about some hardwoods, is that you will not need the same dimension of material to have the same strength as 2X framing lumber.
The sliding dovetails are ideal for the cross members into the side rails. To use the same joint for the attachment of the legs would produce a weak joint in my opinion, I have seen it fail in pedestal table legs.
To dissemble this in time, and to ease the assembly, which sliding dovetails can be a bear to slide together, I suggest tapering the dovetail so as it goes in, the joint gets tighter, it doesn't need much, a 1/16th of an inch over 4 inches on each side would dramatically increase the ease of assembly/disassembly. A router jig with a bushing guide on the router would make the female cuts in the rails, and a router table with a tall fence and a shim on the appropriate corner of the support for the slats would cut the male dovetail. A push bock would be handy to control the top heavy stock for this cut.
Best Answer
Glue is rarely a bad thing to add to a (permanent) joint. Pocket hole screws are plenty strong on their own for most typical applications, but adding glue only makes the joint stronger. Plywood is very strong and very stable (two big reasons for using it), so there's no concern related to that.
One potential problem that may develop as a result of using glue is getting the joint to line up nicely, especially while screwing in the pocket screws. Glue acts as a lubricant here, allowing the two pieces to slide around quite a bit during clamping. If the two pieces are not clamped very securely, they will move when driving in the screws. If you can come up with some kind of registration / alignment system it will make the whole process much easier. Use biscuits, dominoes, rabbets (UK: rebates) (even a 1/16" deep rabbet would aid alignment), whatever to keep the apron aligned on the tabletop.